Final practice qs
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The document contains 25 practice questions related to business mathematics. The questions cover a range of topics including linear functions, break even analysis, supply and demand curves, and compound interest. Students are asked to write linear equations, estimate values, calculate maximums and minimums, interpret slopes and intercepts, and solve various word problems involving rates of return, future and present values, and annuities.
Final practice qs
- 1. Business Mathematics Practice Questions Q1. In 2000, crude oil production by OPEC countries was 29.2 million barrels per day. In 2002, OPEC crude oil production had risen to about 28.7 million barrels per day. A. Assume that the relationship between years after 1997 and crude oil production is linear over this period. Write an equation of the lines relating year to crude oil production. B. Use the linear equation from part (A) to estimate the crude oil production by OPEC countries in 2001 Q2. A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population P ; grows as a linear function of time t, where t is the number of years after 2003. A. How many students will be enrolled in the school in 2010? B. Find a linear function that relates the student population to the time t. Q3. A small college has 2546 students in 1994 and 2702 students in 1996. Assume that the enrollment follows a linear growth pattern. Let t be the time measured in years and n is the number of enrollments. (t = 0 corresponds to 1990) A. Determine the linear function n=f (t) B. State and interpret the meaning of slope of the function? C. Find n-intercept D. Use the function to predict the enrollment of the college in 1999. Q4. The supply curve for a product is y = 300x + 9000, and the demand curve is y = – 100x + 14000, where x represents the price and y the number of items. At what price will the supply equal demand, and how many items will be produced at that price? Q5. Whackemhard Sports is planning to introduce a new line of tennis rackets. The fixed costs for the new line are $25,000 and the variable cost of producing each racket is $60. If the racket sells for $80, find the number of rackets that must be sold in order to break even. Q6. The Stanley Company is coming up with a new cordless travel shaver just before the Christmas holidays. It hopes to sell 10,000 of these shavers in the month of December alone. The manufacturing variable cost is $3 and the fixed costs $100,000. If the shavers sell for $11 each, how many must be produced to break-even? Q7. A magazine company had a profit of $98,000 per year when it had 32,000 subscribers. When it obtained 35,000 subscribers, it had a profit of $117,500. Assuming that the profit P is linear function of the number of subscribers A. Find the linear function of P. B. What will the profit be if the company obtains 50,000 subscribers? C. What is the number of subscribers to breakeven? Q8. A Multinational firm has been hiring the human resource for different positions Each Personnel Manager will cost around 80,000 in salary, each creative head will cost 100,000 and each Marketing Manager will cost 120,000. The firm has planned to have Rs.2.4 millions for all of these new human resources. Determine: a) the equation which justify the budget (mark each job category as x1, x2 and x3)
- 2. b) If the firm wishes to allocate the entire budget on one type of department, how many persons of each department could be hired? c) If 10 personnel manager and 5 marketing manager will be hired, how many of creative heads could be appointed? Q9. Imagine you are interested in effect of unemployment on street crime Here; % unemployment in area (independent variable) and mean number of muggings per month (dependent variable) y = 4.2 + 0.86x a) Identify and interpret the meaning of slope and intercepts. b) Find the mean number of muggings per month when unemployment in area is 45%. Q10. A candidate for the position of governor of a Midwestern state has an advertising budget of $1.5 million. The candidate’s advisors have identified four advertising options that are newspaper, radio, television and billboards. The costs for these options estimate $1,500, $2,500, $10,000 and $ 7,500 respectively. (assume xi number of units purchased and j: media options i.e. 1,2,3 and 4) a) Write an equation, which requires total advertising expenditure of $1.5 million. b) If it has been determined that 100 newspaper ads, 300 radio ads, and 50 billboards ads will be used, how many tv ads can they purchased? c) If 50 billboard ads are to be purchased, what is the maximum number of newspaper ads that can be purchased? Maximum number of radio ads? TV ads? Q11. The average lifespan of American women has been tracked, and the model for the data is y = 0.2t + 73, where t = 0 corresponds to 1970. a) Identify and interpret the meaning of the slope and y-intercept. b) Find the average life span in 2012. Q12. The equation for the speed (not height) of a ball that is thrown straight up in the air is given by v = 128 – 32t, where v is the velocity (in feet per second) and t is the number of seconds after the ball is thrown. a) Identify and interpret the meaning of the slope and v-intercept.? b) Find the speed just after 1 minute? Q13. The purchaser of a local company has to purchase inventory. Inventory consists of file covers, ball pens, pointers, pencils and paper rims. Price of each file cover is Rs.50, ball pen Rs.5, pointer Rs.75, pencil Rs.5 and paper rim Rs.300. It is necessary that he has to consume all budget of Rs.15000. A. Find the maximum of number of units of each item. B. If there 20 paper rims are required, find the maximum number of units of each item. Q14. Assume that a company knows that the cost to produce x items is given by the cost function C ( x) = x 2 + 5 dollars. It also knows that the revenue from x items is given by the revenue function 800 x R( x) =1000 x +200 . Find A) the concavity of profit function, and B) maximum profit they can expect and how many of these items they have to produce and sell to make this maximum profit. Q15. Given the demand of watches to be p = -3q + 60, how many watches must be sold in order to maximize revenue?
- 3. Q16. If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then its height is a function of time, given by s(t) = -16t2 + 54t. A) What is the concavity of the function B) Calculate the maximum height reached by the ball and the maximum time to cover the height p = 2x + − Q17. The linear demand function for a particular item is given by . Find the quantity for which 50 revenue is maximum Q18. The profit (in thousands of dollars) of a company is given by: P(x) = 5000 + 1000x - 5x2; where x is the amount ( in thousands of dollars) the company spends on advertising. Find: A) the amount, x, that the company has to spend to maximize its profit, and B) Find the maximum profit Pmax. Q19. A company produces three products, each of which must be processed through one department. Table shown below summarizes the labor hours and raw material requirements per unit of each product. Each month there are 1300 labor hours and 4700 pounds of the raw material available. If combined monthly production for the three products should equal 400 units, Determine whether there are any combinations of the three products which would exhaust the monthly availabilities of the labor hour and raw material and meet the production goal of 400 units. product 1 Product 2 Product 3 Labor hours/unit 5 2 4 Pound of raw material/unit 15 10 12 Q20. We plan to invest Rs.2500 at the end of each of the next 10 years. We can earn 8%, compounded interest annually, on all invested funds. Find the future value of this annuity at the end of 10 years? Q21. Compute the compound amount of $1,580 if the appropriate rate is 5.4% and you invest the money for four years? Q22. Mr. Jones proposes to invest $1,880 today and expects to accumulate $2,537 in three years. What is the underlying rate of return on the investment? Q23. If the interest rate is 9.6%, find the future value of $12,000 invested every year for 15 years with the first payment made one year from now. Q24. How much would Apex Corp. have to deposit in a bank today in order to withdraw $6,000 each year for 10 years with an annual interest rate of 6%? Q25. How much must a person 65 years old invest today at 8% interest compounded annually to provide for an annuity of $20,000 at the end of each of the next 15 years?