Solution Manual for Fundamentals of Modern Manufacturing: Materials Processes and Systems, 7th Edition, Mikell P. Groover
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- 5. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. 1.5 One of the dimensions of manufacturing capability is technological processing capability. Define technological processing capability. Answer. The technological processing capability of a plant (or company) is its available set of manufacturing processes. Certain plants perform machining operations, others roll steel billets into sheet stock, and others build automobiles. The underlying feature that distinguishes these plants is the processes they can perform. Technological processing capability includes not only the physical processes, but also the expertise possessed by plant personnel in these processing technologies. Manufacturing Materials 1.6 (A) What are the four categories of engineering materials used in manufacturing? Answer. The four categories of engineering materials are (1) metals, (2) ceramics, (3) polymers, and (4) composite materials, which consist of non-homogeneous mixtures of the other three types. 1.7 What is the definition of steel? Answer. Steel can be defined as an iron–carbon alloy containing 0.02% to 2.11% carbon. Its composition often includes other alloying elements as well, such as manganese, chromium, nickel, and molybdenum, to enhance the properties of the metal. 1.8 What are some of the typical applications of steel? Answer. Applications of steel include construction (e.g., bridges, I-beams, and nails), transportation (trucks, rails, and rolling stock for railroads), and consumer products (automobiles and appliances). 1.9 (A) What is the difference between a thermoplastic polymer and a thermosetting polymer? Answer. Thermoplastic polymers can be subjected to multiple heating and cooling cycles without substantially altering the molecular structure of the polymer. Thermosetting polymers chemically transform (cure) into a rigid structure on cooling from a heated plastic condition. 1.10 What is the defining characteristic or property of an elastomer? Answer. Elastomers are polymers that exhibit significant elastic behavior. Manufacturing Processes 1.11 Manufacturing processes are usually accomplished as unit operations. Define unit operation. Answer. A unit operation is a single step in the sequence of steps required to transform the starting material into a final product. A unit operation is generally performed on a single piece of equipment that runs independently of other operations in the plant. 1.12 In manufacturing processes, what is the difference between a processing operation and an assembly operation? Answer. A processing operation transforms a work material from one state of completion to a more advanced state that is closer to the final desired product. It changes the geometry, properties, or appearance of the starting material. In general, processing operations are
- 6. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. performed on discrete work parts, but certain processing operations are also applicable to assembled items (e.g., painting a spot-welded car body). An assembly operation joins two or more components to create a new entity, called an assembly, subassembly, or some other term that refers to the joining process (e.g., a welded assembly is called a weldment). 1.13 What is the difference between casting and molding? Answer. Casting and molding are both solidification processes. The difference is that casting usually refers to the processing of metals, while molding usually refers to the processing of plastics. 1.14 Particulate processing is generally associated with the processing of which two of the three types of engineering materials? Answer. Metals and ceramics (but not glass ceramics). 1.15 What is the most common reason for heating a metallic workpiece before it is subjected to a deformation process? Answer. To increase its ductility during deformation. 1.16 What is a machining operation? Answer. Machining is a material removal process usually performed on metallic parts, in which excess material is removed from the work part so that what remains is the desired geometry. 1.17 (A) Name the three most important machining operations. Answer. Turning, drilling, and milling. 1.18 What is the most important property-enhancing operation? Answer. Heat treatment. 1.19 Identify the four types of permanent joining processes used in assembly. Answer. The four types are welding, brazing, soldering, and adhesive bonding. 1.20 (A) What is a machine tool? Answer. The term developed during the Industrial Revolution, when it referred to power- driven machines used to operate cutting tools previously operated by hand. Modern machine tools are described by the same basic definition, except that the power is electrical rather than water or steam, and the level of precision and automation is much greater today. Production Systems 1.21 (A) Define batch production and describe why it is often used for medium-quantity production. Answer. Batch production is where groups, lots, or batches of materials or parts are processed together through the manufacturing operations. All units in the batch are processed at a given station before the group proceeds to the next station. In a medium or low quantity production situation, the same machines are used to produce many types of products. Whenever a machine switches from one product to another, a changeover occurs.
- 7. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. The changeover requires the machine setup to be torn down and set up for the new product. Batch production allows the changeover time to be distributed across a larger number of parts and hence reduce the average operation time per part. 1.22 With which production quantity range is cellular manufacturing most closely associated? Answer. Medium production quantity range. 1.23 Name two departments that are typically classified as manufacturing support departments. Answer. A common organizational structure includes the following three manufacturing support departments: (1) manufacturing engineering, (2) production planning and control, and (3) quality control. Manufacturing Economics 1.24 What is the difference between sequential batch processing and simultaneous batch processing? Answer. In sequential batch processing, the parts in the batch are processed one after the other. In simultaneous batch processing, all of the parts in the batch are processed together at the same time. 1.25 What are overhead costs in a manufacturing company? Answer. Overhead costs consist of all of the expenses of operating the company other than material, direct labor, and equipment. 1.26 Name and define the two categories of overhead costs in a manufacturing company. Answer. The two categories are (1) factory overhead and (2) corporate overhead. Factory overhead consists of the costs of running the factory excluding materials, direct labor, and equipment. This overhead category includes plant supervision, maintenance, insurance, heat and light, and so forth. Corporate overhead consists of company expenses not related to the factory, such as sales, marketing, accounting, legal, engineering, research and development, office space, utilities, and health benefits. 1.27 (A) What is meant by the term availability? Answer. Availability is a reliability term which is simply the proportion uptime of the equipment. Additional Review Questions for Instructor Use 1.1 What are the differences between primary, secondary, and tertiary industries? Give an example of each category. Answer. A primary industry is one that cultivates and exploits natural resources, such as agriculture or mining. A secondary industry takes the outputs of primary industries and converts them to consumer and capital goods. Examples of secondary industries are textiles and electronics. A tertiary industry is in the service sector of the economy. Examples of tertiary industries are banking and education. 1.2 Annual production quantities made by a factory can be classified into three ranges. Name the three ranges and the approximate quantities of parts associated with each range.
- 8. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Answer. The three ranges are (1) low production, with quantities in the range 1 to 100 parts; (2) medium production, with quantities in the range 100 to 10,000 parts; and (3) high production, with quantities in the range 10,000 to over a million parts. 1.3 Define plant capacity. Answer. Plant capacity, a.k.a. production capacity, is the maximum rate of production output that a plant can achieve under assumed operating conditions. Operating conditions refer to the number of shifts per week, hours per shift, direct labor manning levels in the plant, and so on. 1.4 One of the three general types of processing operations is shaping operations, which are used to create or alter the geometry of the work part. What are the four categories of shaping operations? Answer. The four categories of shaping operations are (1) solidification processes, in which the starting material is a heated liquid or semifluid that cools and solidifies to form the part geometry; (2) particulate processing, in which the starting material is a powder, and the powders are formed and heated into the desired geometry; (3) deformation processes, in which the starting material is a ductile solid (commonly metal) that is deformed to shape the part; and (4) material removal processes, in which the starting material is a solid (ductile or brittle), from which material is removed so that the resulting part has the desired geometry. 1.5 What is the difference between net shape processes and near net shape processes? Answer. Net shape processes are manufacturing processes that transform nearly all of the starting material into product and require no subsequent machining to achieve final part geometry. Near net shape processes are ones that require minimum machining to produce the final shape. 1.6 What are the three types of surface processing operations? Answer. (1) Cleaning, (2) surface treatments, e.g., sand blasting, and (3) coating and thin film deposition, e.g., electroplating, painting, physical vapor deposition. 1.7 What is the difference between special purpose and general purpose production equipment? Answer. General-purpose equipment is more flexible and adaptable to a variety of jobs. It is commercially available for any manufacturing company to invest in. Special-purpose equipment is usually designed to produce a specific part or product in very large quantities. Another reason may be because the process is unique and commercial equipment is not available. Some companies with unique processing requirements develop their own special purpose equipment. 1.8 What is the difference between a process layout and a product layout in a production facility? Answer. A process layout is one where the machinery in a plant is arranged based on the type of process it performs. To produce a product it must visit the departments in the order of the operations that must be performed. This often includes large travel distances within the plant. A process layout is often used when the product variety is large and the operation
- 9. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. sequences of products are dissimilar. A product layout is one where the machinery is arranged based on the general flow of the products that will be produced. Travel distance is reduced because products will generally flow to the next machine in the sequence. A product layout works well when all products tend to follow the same sequence of production operations. 1.9 What is the difference between fixed costs and variable costs? Answer. A fixed cost remains constant for any level of production output, whereas variable costs are paid for as they are used. The cost of the factory and equipment are fixed costs. Direct labor and materials that are used to produce the product are variable costs. Problems Solutions to problems labeled (S) are immediately available to students. Manufacturing Economics 1.1 (S) A company invests $800,000 in a piece of production equipment. The cost to install the equipment in the plant = $35,000. Anticipated life of the machine = 12 years. The machine will be used eight hours per shift, five days per week, 50 weeks per year. Applicable overhead rate = 20%. Assume availability = 100%. Determine the equipment cost rate if the plant operates (a) one shift per day and (b) three shifts per day. Solution: (a) For a one-shift operation, hours of operation per year H = 50(1)(5)(8) = 2000 hr/yr. Ceq = (800,000 + 35,000)(1.20)/(60 12 2000) = $0.696/min = $41.75/hr (b) For a three-shift operation, hours of operation per year H = 50(3)(5)(8) = 6000 hr/yr. Ceq = (800,000 + 35,000)(1.20)/(60 12 6000) = $0.232/min = $13.92/hr Note the significant advantage the company has if it runs 24 hr/day rather than one shift. 1.2 A production machine was purchased six years ago for an installed price of $530,000. At that time it was anticipated that the machine would last 10 years and be used 4000 hours per year. However, it is now in need of major repairs that will cost $125,000. If these repairs are made, the machine will last four more years, operating 4000 hours per year. Applicable overhead rate = 30%. Assume availability = 100%. Determine the equipment cost rate for this machine. Solution: The cost rate under the original conditions was the following: Ceq = 530,000(1.30)/(60 10 4000) = $0.287/min = $17.23/hr The repairs will add to that cost rate as follows: Ceq = 125,000(1.30)/(60 4 4000) = $0.169/min = $10.16/hr The repaired machine has a cost rate Ceq = 0.287 + 0.169 = $0.456/min = $27.36/hr 1.3 Instead of repairing the machine in Problem 1.2, a proposal has been made to purchase a new machine and scrap the current machine at a zero salvage value. The new machine will have a production rate that is 20% faster than the current equipment, whose production rate = 12 parts per hour. Each part has a starting material cost = $1.33 and a selling price = $6.40. All parts produced during the next four years on either machine can be sold at this price. At the end of the four years, the current machine will be scrapped, but the new machine would still be productive for another six years. The new machine costs $700,000 installed, has an anticipated life of 10 years, and an applicable overhead rate of 30%. It will
- 10. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. be used 4000 hours per year, same as the current machine. The labor rate for either alternative = $24.00/hr which includes applicable overhead costs. Assume availability = 100% and scrap rate = 0. Which alternative is more economical using total profit over four years as the criterion, (a) repairing the current machine or (b) purchasing the new machine? Solution: (a) The first alternative is to repair the current machine. The cost rate was determined in the solution to Problem 1.2. Repeating here, the original cost rate is calculated as follows: Ceq = 530,000(1.30)/(60 10 4000) = $0.287/min = $17.23/hr The repairs will add to that cost rate as follows: Ceq = 125,000(1.30)/(60 4 4000) = $0.169/min = $10.16/hr The repaired machine has a cost rate Ceq = 0.287 + 0.169 = $0.456/min = $27.36/hr Labor cost = $24.00/hr (given) Given that annual hours of operation = 4000, total cost of production on this machine is calculated as follows: TC = 4000(24.00 + 27.36) = $205,440/yr At a production rate of 12 pc/hr and operating 4000 hr/yr, annual output = 4000(12) = 48,000 pc/yr Total revenue = 48,000(6.40 – 1.33) = $243,360/yr. Total profit over four years = 4(243,360 – 205,440) = $151,680 (b) The second machine has an equipment cost rate determined as follows: Ceq = 700,000(1.30)/(60 10 4000) = $0.379/min = $22.75/hr Labor cost = $24.00/hr (given) Given that annual hours of operation = 4000, total annual cost of production on this machine is TC = 4000(24.00 + 22.75) = $187,000/yr Production rate on the new machine is 20% faster, so production rate = 12(1.20) = 14.4 pc/hr At 14.4 pc/hr and operating 4000 hr/yr, annual output = 4000(14.4) = 57,600 pc/yr Total revenue = 57,600(6.40 – 1.33) = $292,032/yr. Total profit over four years = 4(292,032 – 187,000) = $420,128 Conclusion: The new machine should be purchased and the old machine scrapped. 1.4 (S) A machine tool is used to machine parts in batches (sequential batch processing). In one batch of interest, the starting piece is a casting that costs = $8.00 each. Batch quantity = 75. The actual machining time in the operation = 5.66 min. Time to load and unload each workpiece = 2.0 min. Cost of the cutting tool = $4.00, and each tool must be changed every 25 pieces. Tool change time = 1.5 min. Setup time for the batch = 1.75 hr. Hourly wage rate of the operator = $16.00/hr, and the applicable labor overhead rate = 45%. Hourly equipment cost rate = $32.00/hr, which includes overhead. Assume availability = 100% and scrap rate = 0. Determine (a) the cycle time for the piece, (b) average hourly production rate when setup time is figured in, and (c) cost per piece. Solution: (a) Processing time To = 5.66 min, part handling time Th = 2.0 min, and tool handling time Tt = 1.50 min/25 = 0.06 min. Tc = 5.66 + 2.00 + 0.06 = 7.72 min (b) Average production time per piece including setup time Tp = 1.75(60)/75 + 7.72 = 9.12 min Average hourly production rate Rp = 60/9.12 = 6.58 pc/hr
- 11. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. (c) Equipment cost rate Ceq = $32.00/60 = $0.533/min. Labor cost rate CL = 16.00(1.45) = $23.20/hr = $0.387/min Cost of tooling Ct = 4.00/25 = $0.16/pc Finally, cost per piece Cpc = 8.00 + (0.533 + 0.387)(9.12) + 0.16 = $16.55/pc 1.5 A stamping press produces sheet-metal stampings in batches. The press is operated by a worker whose labor rate = $15.00/hr and applicable labor overhead rate = 42%. Cost rate of the press = $22.50/hr and applicable equipment overhead rate = 20%. In one job of interest, batch size = 400 stampings, and the time to set up the die in the press takes 75 min. The die cost $40,000 and is expected to last for 200,000 stampings. Each cycle in the operation, the starting blanks of sheet metal are manually loaded into the press, which takes 42 sec. The actual press stroke takes only 8 sec. Unloading the stamping from the press takes 13 sec. Cost of the starting blanks = $0.23/pc. The press operates 250 days per year, 7.5 hours per day, but the operator is paid for 8 hours per day. Assume availability = 100% and scrap rate = 0. Determine (a) cycle time, (b) average production rate with and without setup time included, and (c) cost per stamping produced. Solution: (a) Cycle time Tc = 42 + 8 + 13 = 63 sec = 1.05 min (b) Including setup time, Tp = 75/400 + 1.05 = 1.2375 min Rp = 60/1.2375 = 48.485 pc/hr Excluding setup time, Rc = 60/1.05 = 57.143 pc/hr (c) Equipment cost rate Ceq = 22.50(1.20)/60 = $0.45/min Die cost per piece Ct = 40,000/200,000 = $0.20/pc Labor cost rate CL = 15.00(1.42)/60 = $0.355/min This labor cost should be adjusted for the fact that although the press operates 7.5 hr/day, the operator is paid for 8 hr. CL = 0.355(8/7.5) = $0.379 Finally, cost per stamping Cpc = 0.23 + (0.379 + 0.45)(1.2375) + 0.20 = $1.456/pc 1.6 (S) In a long-running high-production operation, the starting work material cost = $0.65/pc, and cycle time = 1.28 min. Equipment cost rate = $44.00/hr, and labor cost rate = $28.00/hr. Both rates include overhead costs. Tooling cost = $0.05/pc. Availability of the production machine = 95%, and the scrap rate = 4%. Determine (a) production rate and (b) finished part cost. Solution: (a) Production rate, including effect of availability (60/1.28)(0.95) = 44.53 pc/hr However, because of the 3% scrap rate, the production rate of acceptable parts is Rp = 44.53(1 0.04) = 42.75 pc/hr (b) Factoring in availability and scrap rate, part cost is Cpc = 0.65/0.96 + ((44 + 28)/60)(1.28/(0.95 0.96)) + 0.05 = $2.41/pc 1.7 Using the data from the previous problem, solve for the production rate and part cost if the machine availability = 100% and scrap rate = 0%. Solution: (a) Production rate with 100% availability Rp = (60/1.28) = 45.0 pc/hr With 0% scrap rate, Rp = 45.0(1 0.03) = 45.0 pc/hr (b) Cpc = 0.65 + ((44 + 28)/60)(1.28) + 0.05 = $2.24/pc
- 12. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. 1.8 The starting work part costs $2.00 in a sequential batch production operation. Batch quantity = 100 parts. Each cycle, part handling time = 0.40 min, and operation time = 1.52 min. Setup time = 50 min. Equipment cost rate = $30.00/hr, and labor cost rate = $18.00/hr, including overhead costs. There is no tool change or tool cost in the operation. The machine tool is 100% reliable, and scrap rate = 2%. Determine (a) production rate, (b) finished part cost, and (c) number of hours required to complete the batch. Solution: (a) Tc = 1.52 + 0.40 = 1.92 min/pc Given q = 2%, the starting quantity of parts Qo = 100/0.98 = 102.04 rounded to 102 pc Determine batch time, including setup time. Tb = 50 + 102(1.92) = 50 + 195.84 = 245.84 min/batch = 4.097 hr Average production rate of parts Rp = 100/4.097 = 24.41 pc/hr Average production rate of acceptable parts Rp = 24.41(1 0.02) = 23.92 pc/hr (b) Now determine batch cost, including setup time. Cb = 102(2.00) + ((18 + 30)(4.097) = 204.00 + 196.66 = $400.66/batch Cpc = 400.66/100 = $4.007/pc Alternative calculation of Cpc: Cpc = 2.00/0.98 + ((18 + 30)/60)(50/100) + ((18 + 30)/60)(1.92/0.98) Cpc = 2.041 + 0.40 + 1.567= $4.008/pc (c) Time to complete the batch was computed in part (a) as Tb = 245.84 min = 4.097 hr 1.9 In a simultaneous batch processing operation, batches of parts are subjected to a heat treatment process that takes 37.0 min. The batch size each cycle = 120 parts. Each starting piece has a material cost of $1.68. It takes 15 min to load the parts into the furnace and 12 min to unload them onto a moving conveyor. A 2-min changeover time is allowed between batches. The furnace is maintained at the desired temperature for successive batches. Its cost rate = $54/hr. Determine the (a) cycle time, (b) average processing rate per part, and (c) part cost at the completion of the heat treatment process. Solution: (a) Tc = 2.0 +37.0+15.0 + 12.0= 66.0 min/batch (b) Average processing rate Rp = 120/66 = 1.818 pc/min = 109.09 pc/hr (c) Cpc = 1.68 + 54/109.09 = $2.175/pc 1.10 Using the data from the previous problem, determine the (a) cycle time, (b) average processing rate per part, and (c) part cost at the completion of the heat treatment process, if there is a 5% scrap rate during the heat treatment. Solution: (a) Tc = 2.0 +37.0+15.0 + 12.0= 66.0 min/batch (b) Average processing rate Rp = 120/66 = 1.818 pc/min = 109.09 pc/hr Processing rate of acceptable parts Rp = 109.09(1 – 0.05) = 103.64 pc/hr (c) Cpc = 1.68/(1 – 0.05) + (54/103.64) = $2.289/pc 1.11 During a particular 40-hour week of an automated production operation, 381 acceptable (non-defective) parts and 17 defective parts were produced. The operation cycle consists of a processing time of 5.23 min, and a part handling time of 0.58 min. Every 50 parts, a tool change is performed, and this takes 4.2 min. The machine experienced several breakdowns
- 13. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. during the week. Determine (a) hourly production rate of acceptable parts, (b) scrap rate, and (c) availability (proportion uptime) of the machine during this week. Solution: (a) Production rate of acceptable parts Rp = 381/40 = 9.525 pc/hr (b) Total parts processed during the week Qo = 381 + 17 = 398 pc Scrap rate q = 17/398 = 0.0427 = 4.27% (c) Cycle time of the unit operation Tc = 5.23 + 0.58 + 4.2/50 = 5.895 min Total uptime during the week = 398(5.895) = 2345.8 min = 39.097 hr Proportion uptime A = 39.097/40 = 0.977 = 97.7% Additional Problems for Instructor Use 1.1 A plastic molding machine produces a product whose annual demand is in the millions. The machine is automated and used full time just for the production of this product. The molding cycle time = 45 sec. No tooling is required other than the mold, which cost $100,000 and is expected to produce 1,000,000 moldings (products). The plastic molding compound costs $1.20/lb. Each molding weighs 0.88 lb. The only labor required is for a worker to periodically retrieve the moldings. Labor rate of the worker = $18.00/hr including overhead. However, the worker also tends other machines and only spends 20% of his time on this machine. Setup can be ignored because of the long production run. The molding machine was purchased for $500,000 installed, its anticipated life = 10 years, and it operates 6,000 hours per year. Equipment overhead rate = 30%. Availability = 100% and scrap rate = 0. Determine (a) the hourly production rate of the machine, (b) annual quantity of product molded, and (c) cost per piece. Solution: (a) With a cycle time Tc = 45 sec = 0.75 min, Rp = 60/0.75 = 80 pc/hr Factoring in the 98% proportion uptime, Rp = 0.98(80) = 78.4 pc/hr Annual quantity of product = 6,000(78.4) = 470,400 pc/yr (b) Equipment cost rate Ceq = 500,000(1.30)/(60 10 6000) = $0.1806/min Mold cost per piece Ct = 100,000/1,000,000 = $0.10/pc Labor cost rate CL = 18.00(0.20) = $3.60/hr = $0.06/min Finally, cost per piece Cpc = 1.20(0.88) + (0.06 + 0.1806)(0.75) + 0.10 = $1.34/pc 1.2 A production machine operates in a semi-automatic cycle but a worker must tend the machine 100% of the time to load parts. Unloading is accomplished automatically. The worker’s cost rate = $27/hr including applicable labor overhead rate. The equipment cost rate of the machine = $18.00/hr including applicable overhead costs. Cost of the starting parts = $0.15/pc. The job runs several months so the effect of setup can be ignored. Each cycle, the actual process time = 24 sec, and time to load the part = 6 sec. Automatic unloading takes 3 sec. A proposal has been made to install an automatic parts-loading device on the machine. The device would cost $36,000 and would reduce the part loading time to 3 sec each cycle. Its expected life = 4 years. The device would also relieve the worker from full-time attention to the machine. Instead, the worker could tend four machines, effectively reducing the labor cost to 25% of its current rate for each machine. The operation runs 250 days per year, eight hours per day. Assume availability = 100% and scrap rate = 0. Determine the cost per part produced (a) without the parts loading device and (b) with the parts loading device installed. (c) How many days of production
- 14. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. are required to pay for the automatic loading device? In other words find the breakeven point. Solution: (a) Equipment cost rate Ceq = 18/60 = $0.30/min Labor cost rate CL = 27/60 = $0.45/min Without the loading device, Cpc = 0.15 + (0.45 + 0.30)(24 + 6 + 3)/60 = $0.563/pc (b) Cost rate of the device = 36,000/(6042000) = $0.075/min = $4.50/hr With the loading device, Cpc = 0.15 + (0.45/4 + 0.30 + 0.075)(24 + 3 + 3)/60 = $0.394/pc (c) Without the device, Tc = 24 + 6 + 3 = 33 sec = 0.55 min and Cpc = 0.563/pc Rp = Rc = 60/0.55 = 109.1 pc/hr = 872 pc/day With the device, Tc = 24 + 3 + 3 = 33 sec = 0.50 min and Cpc = 0.394/pc At 100% reliability and no setup time, Rp = Rc = 60/0.50 = 120.0 pc/hr = 960 pc/day Let D = number of days of production at which the two alternatives are equivalent. 872(0.563)D = 36,000 + 960(0.394)D 490.9D = 36,000 + 378.2D (490.9 – 378.2)D = 112.7D = 36,000 D = 319.5 round to 320 days 1.3 In a sequential batch-processing operation, the starting work part costs $4.50 each. Batch quantity = 65 parts. Part handling time each cycle = 2.5 min, and machining time per part = 3.44 min. It takes 75 min to set up the machine for production. Equipment cost rate = $25.00/hr, and labor cost rate = $20.00/hr. Both rates include overhead costs. The cutting tool in the operation costs = $5.75/pc and it must be changed every 18 parts. Tool change time = 3.0 min. Availability of the machine tool = 98%, and the scrap rate = 0. Determine (a) production rate and (b) finished part cost. (c) How many hours are required to complete the batch? Solution: (a) Tc = 3.44 + 2.5 + 3/18 = 6.11 min/pc Given q = 0, the starting quantity of parts Qo = 65 pc Now determine batch time, including setup time and availability, assuming that the availability factor does not apply during setup because the machine is not running. Tb = 75 + 65(6.11)/0.98 = 75 + 405.26 = 480.26 min/batch = 8.004 hr Average production rate of parts Rp = 65/8.004 = 8.121 pc/hr (b) Now determine batch cost, including setup time and availability, assuming that the availability factor does not apply during setup because the machine is not running. The number of cutting tools required = 68/18 = 3.78 rounded up to 4 tools at $5.75 each = $23.00. Cbatch = 65(4.50) + ((20 + 25)(8.004) + 4(5.75) = 292.50 + 360.18 + 23.00 = $675.68/batch Cpc = 675.68/65 = $10.39/pc Alternative calculation of Cpc: Cpc = 4.50 + ((20 + 25)/60)(75/65) + ((20 + 25)/60)(6.11/0.98) + 23.00/65 Cpc = 4.50 +0.865 + 4.676 + 0.354 = $10.395/pc (Close enough!) (c) Time to complete the batch was computed in part (a) as Tb = 480.26 min = 8.004 hr 1.4 A high-production operation was studied during an 80-hr period. During that time, a total of seven equipment breakdowns occurred for a total lost production time of 3.8 hr, and the operation produced 38 defective products. No setups were performed during the period.
- 15. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. The operation cycle consists of a processing time of 2.14 min, a part handling time of 0.65 min, and a tool change is required every 25 parts, which takes 1.50 min. Determine (a) hourly production rate of acceptable parts and (b) scrap rate during the period. Solution: (a) Cycle time of the unit operation Tc = 2.14 + 0.65 + 1.50/25 = 2.85 min Hours of production during 80 hours = 80 – 3.8 = 76.2 hr Total number of parts produced = 76.2(60)/2.85 = 1604 pc Number of acceptable parts produced = 1604 – 38 = 1566 pc Production rate of acceptable parts Rp = 1566/80 = 19.58 pc/hr (b) Scrap rate q = 38/1566 = 0.0243 = 2.43%
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- 17. I VIII t was the beginning of spinning-time in Zanah. The grape crop had been gathered, the bare fields had been raked, and nothing remained to be done outside that could not be accomplished by the men and boys. Therefore the women of the colony were assigned the task of making the linen used in the households at Zanah. Although the very latest machinery had been installed in the mills, it was still the custom among the women to spin the colony sheets and table napery. The large dining-room in the inn had been cleared, and twenty wheels had been distributed here and there for the use of the favored “mothers” privileged to enjoy what was really an annual week of gossip. Gathered in the great dining-room were Mother Schneider, Mother Kaufmann, Mother Werther, and their nearest cronies. It was a bright afternoon, and the sun came in through the vine-covered windows. The door on the wide porch was open, and near it, in the choicest place in the room, sat Mother Schneider busy at her wheel. She paused to put back one of the strings of her black cap and asked: “What say they up at the school-house concerning the lost Bible, Sister Kaufmann?” “They speak naught of it,” replied the sour-visaged woman, as she broke her thread. “Many times have I tried to make Brother Brandt tell me what he really thinks, but thou knowest he hath a way of holding his tongue.” “Walda Kellar hath made a good nurse,” said Mother Werther, who was busy sorting the flax. “Anything that she undertaketh she doeth well.”
- 18. “She hath too much freedom in that sick-room,” declared Mother Schneider. “Yea, she hath,” agreed Mother Kaufmann. “There are many hours that I cannot be there to watch her.” “Thou forgettest that Walda Kellar needeth not watching as do other girls. She who hath been chosen to speak for the Lord surely can be trusted. And then thou knowest she is with her own father.” Mother Werther cast an indignant glance at the wife of the Herr Doktor, who had started the conversation. “I trust not that physician from the outside world,” said Mother Kaufmann. “He hath queer ways that are not like those of the men of Zanah.” “He is always most kind and thoughtful; he treats women with much reverence,” said Mother Werther. “I know him best of all persons in Zanah, for doth he not stay here at the gasthaus?” “Since when didst thou become a good judge of men?” asked Mother Kaufmann, with a taunting laugh that showed her ugly tusks. “The wife who after fifteen years hath not discovered the faults of her husband is not fitted to pass judgment on any man. I do not like that Stephen Everett.” “He is helping Wilhelm Kellar to regain his health,” said a meek, middle-aged woman who sat in a far corner. “It is a fortnight since Brother Kellar was taken ill, and he is still in bed,” said Mother Kaufmann. “Thou forgettest that Brother Kellar hath been nigh unto death,” said Mother Werther. “That doctor from the world is a handsome man,” remarked Gretchen Schneider, who had come in and taken her seat near her mother. “Tut, tut; I am ashamed of thee,” said Mother Schneider, in a tone of reproof. “Thou forgettest that the maidens of Zanah must not look upon men, and must not care whether they be handsome or hideous.”
- 19. “Dost thou find him more comely than Karl Weisel, our respected elder?” inquired Mother Werther; and, despite the scowl of the wife of the Herr Doktor, smothered laughs were heard from various parts of the room. Gretchen Schneider’s pale face flushed. Before she could reply her mother retorted: “Thy words are unseemly, Sister Werther. I bid thee keep silence.” “I have the right of free speech,” the innkeeper’s wife answered; “and there is none in Zanah who doth not know there would have been a wedding long ago if the head of the thirteen elders had not loved his place of authority better than the daughter of the Herr Doktor.” In a moment Mother Schneider flew into a rage, quite inconsistent with the religious principles of Zanah. “Hold thou thy clattering tongue,” she commanded; and for the space of two minutes not a word was spoken in the room. The whirring of the busy wheels alone disturbed the quiet. The entrance of Frieda Bergen fortunately relieved the situation of its tensity. The girl came into the room bearing on her head a bundle of flax, which she deposited before Mother Werther. “This I brought from the station, whither I went with Mother Schmidt,” she said. “Thou shouldst not have been allowed to go to the railroad,” said Mother Kaufmann. “But what didst thou see there?” “A train came by while I stood on the platform. I looked through one of the windows and saw silken-cushioned seats, and mirrors that showed gayly dressed men and women. There was also a car in which were dining-tables. Black men waited on women, who laughed and talked with men. Some of the women wore on their fingers jewels that looked like sparkling glass.” The wheels had all stopped. Every “mother” in the room was listening. “The sparkling glass that thou sawest was what is called a diamond,” said Gretchen Schneider. “Jewels are worn by those who
- 20. have vanity in their souls.” “Truly, the rings were very beautiful,” said Frieda Bergen. “Thou wert ever a foolish maid,” said Mother Schneider, in a tone of severe reproof. “Put out of thy thoughts what thou hast seen to- day. I shall have the Herr Doktor forbid thee from going to the station.” “Nay, Sister Schneider, scold not Frieda. She hath done no harm,” said Mother Werther. “It should not hurt her to get a glimpse of the vanities of the world, for she is well grounded in the faith of Zanah. She knoweth that the costly gauds are but the playthings of sin- ridden women.” Standing in the middle of the room, Frieda Bergen shook her head doubtfully. “Truly, those worldly ones appeared happy,” she said. “There were some that read books and leaned back on velvet cushions. They looked as if they never worked. Some of the women were beautiful. They wore no caps upon their hair. Their frocks were not all alike, as they are here in Zanah.” “See, the daughter of Zanah is touched by the temptations of the world,” said Mother Schneider. “We have heard enough. Begin thy work, Frieda Bergen.” “If what I hear is true, the elders should discipline Frieda,” said Mother Kaufmann, with a sneer. “It hath come to my ears that she hath often spoken with Joseph Hoff.” Frieda Bergen bent her head over her work. A telltale blush overspread her delicate skin, and her hand trembled as she took up her distaff. “Frieda Bergen hath the right to love Joseph Hoff if she chooseth,” said Mother Werther, rising from her chair and walking the length of the room to the place where the girl sat. “Love may be a foolish thing in the eyes of Zanah, but it bringeth its reward.” “Thou art teaching heresy, Sister Werther,” said Mother Schneider. “If the elders knew of thy heterodoxy thou wouldst have to do
- 21. penance through some hard task.” Mother Werther smiled in a tantalizing way. She drew in a long breath as she were about to retort, and then, thinking better of it, went back to her work. “If Frieda is wise she will follow the example of some of us who have served God faithfully all unmindful of man,” said Mother Kaufmann. Her remark was too much for Mother Werther. Dropping her flax, the innkeeper’s wife put her hands upon her hips and laughed. “And hast thou always been unmindful of Gerson Brandt?” she inquired. “Mother, thou shouldst put an end to this unseemly talk,” said Gretchen Schneider. “Yea, thou hast something to fear lest it be remembered how narrowly thou hast escaped love,” said Mother Werther. “Stop thine unruly tongue,” admonished Mother Schneider. “Thou forgettest that in Zanah all men and women are equal,” said Mother Werther. “Thy husband, the Herr Doktor, is enjoying but a brief authority. Thou art not greater than any other woman in the colony.” Mother Schneider gasped in anger, but before she could reply a shadow was cast upon the floor and Walda Kellar entered. Her sweet face wore an untroubled look. She smiled upon all the women gathered in the room. “Something brought me here among you,” she said. “I have but just come from my father’s sick-room, and as I walked long, thinking of the coming Untersuchung, I felt that I wanted once more to spin with the women of Zanah.” “Thou bringest peace with thee,” said Mother Werther. Frieda Bergen rose from her little, low-backed chair, and Walda Kellar seated herself before the girl’s wheel. Silence fell upon the room. The girl’s presence commanded reverence. In her eyes was a peculiar light, and her face was
- 22. radiant. Slowly she began to turn her wheel. “It is very good to be here,” she said, presently. “If the Lord giveth me the tongue of inspiration there will be other tasks for me, and now and then, when I am not quite so strong in the faith as I ought to be, I wonder whether I shall not sometimes be an unworthy instrument of the Lord, because the little things of life, it seemeth, will always have a charm for me. While the great, leather-bound books of Zanah have much to teach me, there are days when my inclinations draw me towards the labors which belong to the women of the colony.” No one answered. For a few moments the wheels whirred again, and not a word disturbed the pleasant hum of industry. Presently Walda’s voice rose in a minor hymn. The deep, rich cadences swelled above the sound of the wheels. It was a weird, plaintive tune to which she sang German words which breathed a prayer for light upon the way that led through the sin-encompassed world. She paused after the first verse. Appearing to forget her work, she clasped her hands in her lap and sang again with such sweetness and such pathos that Mother Werther wiped her eyes. The singing had brought some one to the porch outside, but Walda appeared not to hear the footstep. She sang on and on, and when the last verse died upon her lips she sat very still, as if her soul had gone out with the strange melody. Everett, who had come to the window, looking through the blinds, beheld the prophetess. For the moment the woman was lost, and he felt an overwhelming sense of her aloofness from him. There came to him a full realization of the gulf between him and this woman of Zanah, who belonged so little to the world and so much to heaven. For several minutes he stood fascinated as he gazed upon her, but, summoning all his will-power, he turned away lest he should be discovered spying upon the women of Zanah. As he walked towards the bluffs he met Hans Peter moving along in a leisurely manner. The witchery of Walda’s song was still upon him, and he would have passed the simple one without a greeting, but Hans Peter stepped directly in his path.
- 23. “Thou hast made trouble in Zanah,” said the simple one, staring at him with unblinking eyes and doubling up one fat fist. “The day that thou goest hence to the wicked world where thou belongest will be a happy one.” “You speak with but scant respect for the stranger within your gates,” said Everett, who was amused by the vehemence of the village fool. Hans Peter removed his ragged cap. “Thou hast brought sorrow to Gerson Brandt,” he continued, “for thou wouldst have taken the Bible that he was making beautiful for Walda Kellar.” Everett studied the odd little figure before him for a moment. It was the first time that Hans Peter had betrayed, in manner or countenance, the least trace of emotion. Even now, as the simple one stood blinking his eyes, the man of the world could not comprehend his motive in making the unexpected accusation. “You seem almost excited, Hans Peter,” said Everett, presently, when the boy had begun to show that the silence was uncomfortable. “And why are you concerned about the Bible?” “The school-master setteth great store on the Sacred Book,” replied the simple one. “He hath been kind to me, and I like not to see him troubled.” “And is not every one kind to you, Hans Peter?” The simple one thrust his hand into his deep pocket and hung his head. “The people of Zanah are many times vexed with the fool,” he said. “They have scant patience with one who believes not as they do. In all the colony there are only three who seem to forget that Hans Peter is the village fool.” “And who are they? Gerson Brandt is one, I know. Who are the others?” “The prophetess of Zanah and Mother Werther.” “And do you not believe in the prophetess of Zanah? Have you not faith that she will be the inspired one?”
- 24. “Why do you question the village fool?” asked Hans Peter, suddenly, wary lest he should tell something that he wished to conceal. “Thou knowest that to all the colony Walda Kellar is the revered one. Truly, she walketh near to God.” “Then perhaps some day she will lead you into the full faith of Zanah?” said Everett. But the fool shook his head. “Hans Peter loveth earth, not heaven. He would not be wise as the men of Zanah are wise, for verily their wisdom bringeth them no joy.” “Hans Peter, you speak as one who has much knowledge, after all. I am beginning to think that you are the wisest man in the colony.” “If there is wisdom in knowing one is a fool and being content in his own folly, then am I wise. They say that the fool is often given the power of prophecy; and when I was carving the day of the month upon one of the gourds I keep to help my memory, there came to me the fear that something was coming to Zanah through thee. I ran to seek thee that I might give warning of the trouble thou art bringing to the colony.” Everett reached into the pocket of his coat, took out a cigar, and lighted it. “Perhaps you will be kind enough to tell me in just what way I am to bring more trouble to Zanah,” he said, with a smile. “I had nothing to do with the loss of the Bible, for I have refused to buy it, and I give you my word now, Hans Peter, that I will never take it away from Gerson Brandt.” “Thy word is not needed now,” answered the fool. “The Bible is where thou canst not get it.” “And you know where it is,” said Everett, so quickly that the fool was taken off his guard. “And if I do, no one shall find it,” the simple one declared, with a gesture of his arm and a stamp of his bare foot. “Don’t you think it would be wise for you to take back the Bible to Gerson Brandt?” Everett inquired, walking a few steps to his right, where there was a great tree against which he leaned.
- 25. “If the Bible could be found it would not again be put in Gerson Brandt’s hands. It is better that it should be lost forever than that he should see it owned by another man.” “Why is this Bible so precious to the school-master? Can’t you tell me, Hans Peter? Perhaps I may help you to restore it to him. You see, I might buy it and give it back to Gerson Brandt.” “No man in Zanah can own anything. If the Bible should be given to Gerson Brandt it would still belong to the colony, and it could be sold again.” The simple one had thrown himself upon the ground, and, with chin in his hands and elbows dug deeply in the earth, he appeared to be thinking. “Tell me about the Bible,” urged Everett, and he waited as impatiently for the village fool to speak as if some matter of tremendous importance to him, the man of affairs out in the great world, hung in the balance. There was something almost absurd in the contrast between the two who talked there in the summer afternoon. Stephen Everett was a man to be noticed anywhere. It was not altogether his physical beauty that invariably commanded attention; he had an unusual charm of personality. Hans Peter, with his long, straight tow hair tangled upon his big, round head, kicked his earth-stained feet in the air as he lay at length upon the ground. His blue cotton shirt, torn down the back, revealed a strip of white skin, and his baggy trousers were held by the one button which attached them to a knitted suspender. The pocket in the back of his trousers bulged with one of the gourds that he carried with him wherever he went. “I am waiting for you to tell me about the Bible,” Everett remarked, when he had smoked half of his cigar. Hans Peter reached back and removed the gourd from his pocket. Then, sitting up, he began to examine it carefully. “It was long ago that it came to Hans Peter one day, as he watched Gerson Brandt at work with his bright inks, that the school- master’s thoughts were on Walda Kellar as he made the gay letters in the great book. Lest the fool might forget, he marked on his
- 26. gourd some lines to make him remember. Many times after that he saw that the school-master was praying for her who would be inspired. Hans Peter knew that the Bible was for Walda Kellar, and that the school-master meant it for her to read every day when she should become an instrument of the Lord. That is why Gerson Brandt loved the Bible. That is why no other man should have it.” Everett left his place at the tree, and, pacing back and forth, pondered for a few moments upon the information that the simple one had given him. “Ah, the school-master is a second father to Walda Kellar, I suppose?” he said, presently, casting a furtive glance at the fool. “Nay, he hath not years enough to make it right he should love her as a father,” declared Hans Peter, nodding his head. “The simple one hath been taught that love is a wicked thing, but there is in Gerson Brandt’s heart something that may be love, like that with which he worships angels.” “Again I tell you, Hans Peter, you are the wisest of all the colonists in Zanah,” said Everett. “There, go about your errands.” “But thou wilt promise not to buy the Bible, even if it is ever found?” said Hans Peter, coming close to Everett and lowering his voice. “Yes, yes; you have my word for it. I shall not buy it unless it is to aid Gerson Brandt,” Everett replied. “And, Hans Peter, give me your hand. I pledge my word.” The fool hesitatingly put out his fat, work-hardened hand, and Everett gave it a hearty clasp.
- 27. W IX ilhelm Kellar lay propped up in the four-posted bedstead that stood in his little alcove. His thin face showed the effect of his illness, and the hand that played with the flowered coverlet was thin to the point of translucency. His long, white hair was brushed straight back from his high forehead; his eyes, which had sunk deep into their sockets, wandered restlessly. “Walda, where art thou?” he said, in a thick, indistinct voice. Walda pushed back the chintz curtains that divided the alcove from the larger room, and, kneeling beside her father, took one of his hands in hers. “I have been thinking of the Untersuchung, daughter,” said the sick man, “and I pray that I may be able to be present when the spirit descends upon thee.” “Thou wilt be well in another month,” said Walda, soothingly, as she stroked the white hair. “The physician hath said that thou canst soon leave thy bed.” “But the Untersuchung is only two weeks off,” said Wilhelm Kellar. “It may be that if strength is not vouchsafed me so that I may walk again a litter can be made for me. I would be carried to the place if I cannot go there myself.” “There is some talk that the Untersuchung may be delayed for a month,” said Walda, “and then thou wilt surely be able to take thy place among the elders.” “It would be well, indeed, to postpone the Untersuchung, for thou hast been much distracted from thy meditations by my illness.”
- 28. “Nay, nay, father. Strange thoughts have come to me since I have been sitting here many hours a day in this room. Never hath heaven seemed so near to me.” “It is well, indeed, that thou hast never been touched by earthly love,” said the old man, scanning the face of his daughter. “It was to keep thee free from it that I brought thee here when thou wast a little child, for it putteth waywardness and frowardness into the heart of a woman. Since I have been near to death it hath been shown to me that I must warn thee again lest thou some time feel its evil influence. Thy mother forgot all duty. She forfeited her soul for love.” The old man spoke with intense feeling; he trembled as a long- controlled emotion swept over him. It was as if he had unlocked the flood-gates of a passion barred for many years within his heart. “What dost thou mean, father?” asked Walda, rising to her feet. A deathly pallor overspread her face, but the habit of repression, taught so persistently in Zanah, prevented her from showing the terror with which his words smote her. “I mean,” said Wilhelm Kellar, drawing a quick breath—“I mean—” But suddenly his tongue stiffened and refused to frame the words he would have spoken. “Thou wilt make thyself more ill,” said Walda. “Think not of the past.” Taking a pewter cup of water from the table, she moistened his lips. The old man clinched his fists and closed his eyes. He lay as if he were dead. The frightened girl ran to the door of the room to summon help. Stephen Everett was coming up the stairs. “Oh, hasten to my father!” Walda implored. “I fear greatly for him.” Everett went to the bedside, felt the old man’s pulse, listened to his heart, and discovered that his patient had, indeed, some serious symptoms. “Has anything happened to disturb your father?” he asked, turning to Walda, who stood with hands clasped around one of the head- posts of the bed while she watched him with breathless interest.
- 29. “He began to talk to me of the past,” said the girl, with hesitation, and Everett saw tears in her eyes. “And he recalled some memory that troubled him?” asked Everett. “Yea, yea; he would have told me something of my mother,” said the girl, as she turned to go into the outer room. Everett administered a soothing-potion, and went out of the alcove to find that Walda was sitting by the old carven table with her head bowed upon her hands. “Do not be alarmed,” he said, “your father will recover from this temporary relapse.” His voice and manner were so sympathetic that the girl began to weep. “Be blind to my weakness, O stranger in Zanah,” she said, presently lifting her head proudly and biting her trembling lips. “My faith teacheth me that nothing which belongeth to earth is worth a tear. The people of Zanah are trained to accept the decrees of God. For an hour I have been thinking of self. Strength will be given me to put these rebellious impulses from me.” She went to the window, where the chaffinch was hanging in his wicker cage. “Piepmatz, thou hast no foolish tears; thou canst teach me a lesson that I need; thou art undisturbed by any distrust in thy nature.” Piepmatz, thrusting his head forward, looked out between the bars of his little prison. Then he chirped a cheery note. Everett went close to the cage and whistled to the bird, which paid no attention to him. “If I can be of service to you, you must command me,” he said to Walda Kellar. “You must not think of me as the stranger in Zanah. Have I not earned the right to be called a friend?” He did not look at her as he spoke lest she might be awakened to the fact that he took more than a passing interest in her. “We use not the word friend in Zanah,” said Walda. “Here we are all brothers and sisters. And what dost thou mean by being a friend?” Out in the world Everett had the reputation of being ever ready with words, but when the future prophetess of Zanah looked up at
- 30. him with questioning eyes he was abashed. “I mean,” he began—“I mean that I want you to feel you can trust me even more than if I were a brother of Zanah,” he replied, rather lamely. Walda looked puzzled. “There is none whom I could trust more than the men of Zanah,” she said. “I have been taught by Adolph Schneider and the elders that there is no such thing as friendship between men and women. The Bible telleth that David and Jonathan were friends, but truly I cannot remember that there were men and women in Holy Writ who called each other by that word thou wouldst have me give to thee in my thoughts.” Everett now sought in vain for an argument that he would dare make bold to use. Suddenly he regretted that he had neglected to study the Bible since his Sunday-school days had ended. He tried to think of all the Scripture stories he knew, dimly hoping that somewhere he could recall one that would be a fit illustration. He felt a disgust with himself when he discovered how lamentably ignorant he was. If he could only have commanded a text that would be convincing, he felt that he might be able to win something more than an impersonal gratitude from the future prophetess of Zanah, who had almost ignored him during the fortnight that had passed since he had been serving her father for her sake. “Out in the world there are many friendships between men and women,” he declared. “Then, indeed, must they be sinful,” said Walda, “for I have heard that there be few who serve the Lord with singleness of purpose out there beyond the bluffs.” “Do not condemn the world too severely. Surely you do not think that I am such a wicked man?” His effort to draw attention to himself failed, however, for Walda was gazing out upon the bluffs as if she had forgotten him in thinking of the great world that Zanah barred out.
- 31. “Still thou hast not told me the true meaning of a friend,” she said, presently, and again Everett became aware that somehow he had lost the gift of speech. “Perhaps I cannot find words to make the meaning of friendship plain,” he said, finally, “but I will try to teach you what the word implies.” “Nay, Stephen Everett, it is not right that thou shouldst teach me anything, since thou art of the world, to which thou wilt soon return.” “The world will never be the same to me after I leave Zanah,” said Everett. “Hast thine eyes been opened to its wickedness?” “No. Since I came to the colony I have thought little of the world, but my eyes have been opened to some things to which they were blind before—things that do not belong to the every-day world.” Again he was afraid to let himself look at Walda, and he appeared to be addressing Piepmatz. Walda did not reply to him. She was thinking again of the life beyond the bluffs. “Often have I tried to imagine what life must be outside of Zanah,” Walda remarked, by-and-by, after a long silence. “Now and then stray memories come back to me, for thou knowest I was born in the world, and that I was a little child who brought to the colony recollections of another existence. It is these memories that compel me oftentimes to pray that I may be spared temptation which should never assail a woman of Zanah.” “Surely no temptation could come to you,” said Everett. “Thou knowest little of a woman’s heart. The seeds of vanity are here,” she said, folding her hands upon her breast. “I find pleasure in the flowers and the pretty things that God hath made.” “It seems to me a sin for the colonists to deny its members the highest joys that have been given to men and women,” said Everett. “I have often wondered whether you had any idea of all that you miss here in Zanah.”
- 32. “I miss nothing that is best for my well-being,” said Walda. “Thou wouldst not plant discontent in my heart, wouldst thou, Stephen Everett?” “I would have you enjoy all that is most to be desired in life,” said Everett; and as he spoke he felt for the hundredth time an overwhelming impatience with the creed of the colony which denied to the young and beautiful all that made living worth while. Walda went to the chest of drawers, and, taking her knitting from a little basket, sank upon a low chair, from which she could get a glimpse of her sleeping father. Everett felt that she had dismissed him. He took up his hat and said: “You told me I might call you Walda, so I shall say, Good-night, Walda.” “Good-night,” said the girl. Everett hesitated. “Will you not say, ‘Good-night, Stephen’?” he asked. Walda stopped knitting. “Why wouldst thou have me say thy name again?” she inquired. For the twentieth time Everett was embarrassed. “Because it is the custom of friends to speak one another’s names,” he explained. “But we are not friends,” said Walda. “At least you will repay me for my long stay here in the colony by speaking my name now and then,” he insisted, hypocritically. There was the barest shadow of a smile on the lips of the future prophetess of Zanah. “Good-night, Stephen,” she said; and because he could find no excuse for lingering longer in the quaint room under the eaves, he went away.
- 33. W X ilhelm Kellar’s health mended slowly. Some days he felt strong enough to be lifted out upon the chintz-covered lounge in the large room, but every attempt to hasten convalescence appeared futile, and after a morning spent out of bed he always felt a reaction. On one of his best days he lay on the lounge, which had been pushed into the bay-window. Above his head hung Piepmatz. When Everett came to make the first call of the day, the bird was trilling his one bar of the doxology, with long breaks now and then between the notes. Walda was trimming a plant that stood on the table near which sat Gerson Brandt. The school-master watched the future prophetess intently, and at first he did not notice Everett’s entrance. “My patient must be better,” said Everett, passing to the window, and Walda, turning from the table, answered: “We are happy, indeed, to-day. My father hath already begun to think about his work in the colony.” “You must not be too ambitious,” said Everett, drawing a stool to the foot of the lounge and placing himself where he could study the old man’s face. “I have declared a half-holiday that I may celebrate the return of health to Brother Kellar,” said Gerson Brandt, smiling upon his old friend, who lay, weak and prostrated, among the pillows. At this point Piepmatz abandoned the doxology and burst into a flood of song. “Hush, thou saucy bird,” Walda commanded. She went to the cage and playfully shook her finger at the chaffinch. “See, he knoweth
- 34. there is reason to be glad,” she declared. “Verily he hath much wisdom.” “Piepmatz is something of a philosopher,” remarked Everett. “He makes the best of his imprisonment. Like the people of Zanah, he appears to care little for the great world.” “He hath taught me many a lesson of submission,” said Walda. “Still, his tiny heart is easily touched by worldly things,” said the school-master. “He hath shown a dangerous inclination to take up the song the stranger hath whistled.” “Let me see whether you have forgotten the worldly song.” It was Everett who spoke. Going to the cage he whistled the minor strain of the love-song. Piepmatz proudly imitated him. “You see, I might have been a good school-master if fate had not decreed otherwise,” said Everett, addressing Gerson Brandt. “What is thy work in the world?” asked Walda. “Since my thoughtless plea kept thee here I have often wondered about thy daily labors. At first I thought thou didst tend the sick, but once I heard thee say that thou hadst not yet begun that labor.” “So far I have not done any one thing,” Everett confessed, with a feeling of shame. “How dost thou spend thy days?” the school-master inquired. Everett hesitated before answering. In all his life it had never occurred to him to think how his days were spent. “Since I left college I have travelled a great deal,” he replied, evasively. “And hast thou seen the whole world?” asked Walda. Wonder was written on her face. “I have seen much of it.” Wilhelm Kellar made an inarticulate sound. “Perhaps it disturbeth Brother Kellar to hear thee speak of the wicked world which he left long ago,” said Gerson Brandt. “Like thee, he hath seen it all; he hath wandered over land and sea.”
- 35. “Knowing the world, my father hath kept me safe from it.” Walda had drawn the stool first occupied by Everett close to the head of the lounge, and, sitting near to the sick man, she clasped one of his hands. “Thou knowest, dear, that I have put away from me all vain longings to know aught of life outside of Zanah.” Wilhelm Kellar closed his eyes with a look of contentment. “Didst thou mean me to understand that thou art that abomination of the Lord, an idle and slothful man?” he asked Everett, after a moment of reflection. “I confess that I have not done half my duty,” said Everett, humbly; “but I have spent many years in study; I have dipped into science.” “Science? Zanah hath naught to do with science,” said Gerson Brandt. “Science would reveal the mysteries of nature that the Lord hath hidden from his people.” “Don’t you think that the man who inquires just how the tiny body of Piepmatz has had its origin in the egg, how the bones and muscles that form the wing give him the power of flight, and how his mite of a brain is made to be the home of at least a fragment of intelligence has a wider conception of the omnipotence of God than he who knows nothing of what you call the secrets of nature?” asked Everett. “I would not place my judgment against the judgment of Zanah,” said Gerson Brandt. “And yet when I was a boy I learned about the growth of a flower, and my soul was quickened with a new impulse towards worship.” “They tell me there is a magic force called electricity that is now performing what would once have been called miracles,” said Walda. It seemed incredible to Everett that, notwithstanding all the barriers placed between Zanah and the outside world, it could be possible so completely to shut out all that was modern.
- 36. “Yes; electricity propels cars; it gives men the power to talk when they are hundreds of miles apart; it sends words across the continent, literally, with lightning rapidity. You know the latest achievement of science is the discovery of the x-ray, by which it is possible to look through a man’s body so that the bones are visible.” “How strange it all is!” exclaimed Walda, who was still stroking her father’s hand. “The wisdom of the world is so great that no one man can understand more than the smallest fragment of it,” averred Gerson Brandt. Walda was lost in thought for another moment or two. “Thou makest it clear to me that we people of Zanah must seem strange, indeed, to thee.” She spoke slowly. “According to thy standard, I, who am thought wise enough to be chosen prophetess of the colony, must be ignorant and childish. Out in the world they would jeer at me, would they not?” “Thou wilt have a wisdom that the world cannot give,” said Gerson Brandt. “Thou shalt be spared from contact with the mammon of unrighteousness.” “Nay, Gerson, it seemeth to me there must be good men in the world. Stephen Everett, the stranger who hath come to us, belongeth not to those who are bound to the idols of sin.” Everett, who had been sitting in one of the splint-bottomed arm- chairs, was touched by the girl’s artless words. He rose to his feet and responded quickly: “According to Zanah’s standard I may not be a good man, but out in the world I am not singled out as one of the profligates. I hold honor dear. You people of Zanah may trust me.” “We have trusted thee,” said Gerson Brandt. “We have prayed much over thee, and it hath been revealed to us that thou wert sent from the Lord. We trust thee so much that we have let thee speak to Walda Kellar, who hath never known any one belonging to the world.”
- 37. Gerson Brandt stood up and faced Everett. An intensity in his tone gave his words strong emphasis. Wilhelm Kellar turned his head on his pillow, and his sunken eyes stared at Everett as if they would read his uttermost thoughts. A deep flush overspread Everett’s face, and the realization swept over him that perhaps he might have it in his power to disturb all the plans of Zanah by turning Walda Kellar’s thoughts away from what he regarded as the superstition of the colony. Human nature is contradictory, and Gerson Brandt’s words presented clearly a temptation that had but vaguely suggested itself to him. He could appear not to recognize the insinuation conveyed by the school-master, and therefore he replied, evasively: “My intentions are good. It was an unselfish motive that prompted me to remain in the colony. When Wilhelm Kellar has recovered I shall go away, and you will all forget that I ever came to Zanah.” “Nay, we shall not forget thee,” said Walda. “We shall always be grateful to thee.” The conversation was interrupted at this point by the appearance of Karl Weisel. He had scarcely finished his greetings when Mother Kaufmann and Gretchen Schneider came into the room. “How is it that the prophetess of Zanah hath time to spend in the company of men?” asked Mother Kaufmann. “It might be better to pass the days alone, praying and reading the Bible.” “How is it that Mother Kaufmann dares to speak thus sharply in the presence of the woman chosen to guide the colony of Zanah?” retorted Gerson Brandt. “I like not this dispensation which permits Walda Kellar to be brought under the influence of a sinful man of the world.” Mother Kaufmann spoke in her guttural German. She had advanced close to Gerson Brandt. “The colony is not ruled by old women, and thy likes weigh little in Zanah,” declared Karl Weisel, whose chair had been drawn near to the one chosen by Gretchen Schneider. “If Zanah were ruled by old women the head of the thirteen elders would not be coveting the daughter of the Herr Doktor,” said Mother
- 38. Kaufmann, losing all caution in her anger. Gretchen Schneider’s thin face turned a livid yellow, and Karl Weisel sprang forward as if he would like to grasp the woman by the throat. “Peace, children of Zanah,” commanded Walda, rising in majestic indignation. “Your words are shameful. Put away from you the spirit of contention.” Wilhelm Kellar had made an effort to speak, but in the excitement of the moment his tongue refused to frame the words. Everett, looking at him, saw that there were beads of perspiration on his brow and that he looked exhausted. “Send these people out of the room,” he said to Gerson Brandt. “Wilhelm Kellar must be kept quiet.” He went to the table, where he began to mix a soothing draught, while Gerson Brandt dismissed the three visitors. The school-master preceded them out of the room, leaving Walda and Everett to soothe the sick man, who showed signs of extreme exhaustion. When the medicine had been administered, Walda drew together the white curtains and placed a chintz screen before the window. “He looketh almost as if death were near,” she whispered to Everett. “Do not be alarmed,” he replied; “he will soon fall asleep, and when he awakens he will be as well as he was this morning.” The girl bent over her father to watch the faint breathing. The old man’s face was ghastly in its emaciation and pallor. “Thou wilt not leave me yet?” she said, entreatingly. “Sit here with me until I am sure he is slumbering peacefully.” Walda took her place on an old oaken bench above which hung Gerson Brandt’s book-shelves, and Everett drew one of the chairs close to the table, near to the place where Walda sat. Instead of taking up her knitting the girl leaned on the oaken arm of the bench, and with her chin in her hands she became lost in thought.
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