Lesson 24: Optimization II (worksheet)
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The document is a worksheet containing 4 optimization problems: 1) Find the dimensions of a printed rectangular region and advertisement to minimize total area given the printed area is 92 in^2. 2) Find the dimensions of an advertisement to maximize the printed rectangular area given the total area is 120 in^2. 3) Find the dimensions of a rectangular window and semicircular top to maximize the window area given 8 + 2π feet of trim. 4) Find the dimensions of a soda bottle shaped like a cylinder with hemispherical cap that minimizes production cost given the volume is 2 liters.
Lesson 24: Optimization II (worksheet)
- 1. Worksheet for Section 4.5 Optimization II November 25, 2009 1. An advertisement consists of a rectangular printed region plus 1 in margins on the sides and 2 in margins on the top and bottom. If the area of the printed region is to be 92 in2 , find the dimensions of the printed region and overall advertisement that minimize the total area. 2. An advertisement consists of a rectangular printed region plus 1 in margins on the sides and 1.5 in margins on the top and bottom. If the total area of the advertisement is to be 120 in2 , what dimensions should the advertisement be to maximize the area of the printed region? 1
- 2. 3. A Norman window has the outline of a semicircle on top of a rectangle. Suppose there is 8 + 2π feet of wood trim available. Find the dimensions of the rectangle and semicircle that will maximize the area of the window. 2
- 3. 4. A two-liter soda bottle is roughly shaped like a cylinder with a hemispherical cap, and is made from a plastic called polyethylene terephthalate (PET). Its volume is fixed at two liters. What dimensions of the bottle will minimize the cost of production? 3