 ## Review Exercises for Applied Calculus Finite Mathematics & Applied Calculus Topic: Nonlinear Models

Chapter 2 Summary
True/False Quiz
Index of Review Exercises
Everything for Calculus
Everything for Finite Math
Everything for Finite Math & Calculus
Utilities: Function Evaluator & Grapher | Excel Grapher | On-Line Regression Utilty | All Utilities Question 1 The two fraternities Sigma Mu and Epsilon Alpha plan to raise money in a joint effort to benefit homeless people on Long Island. They will sell Jurassic Park T shirts in the student center, but are not sure how much to charge. Sigma Mu treasurer Solo recalls that they once sold 400 shirts in a week at \$8 each, while Epsilon Alpha treasurer Justino claims that, based on past experience, they can sell 600 per week if they charge \$5 each.

(a) Based on the above anecdotal information, construct a linear demand equation for Jurassic Park T shirts, giving weekly sales q as a linear function of unit price p.

(b) At what price should Sigma Mu and Epsilon Alpha sell the T shirts in order to obtain the largest possible revenue?

(c) Approximately how many T shirts would they sell at that price?

Question 2 The proprietor of Delta Nuttal Music Mania Store finds that, when the store offers old Slayer CDs at \$10 per CD, it sells 10,000 discs per week. Dropping the price to \$7.50 per disc has the effect of boosting sales to 17,500 per week. Use this data to set up a demand equation, and determine the unit price (to the nearest cent) the music store should charge to obtain the maximum revenue.

Question 3 Continuing Question 12, suppose that old Slayer CDs cost the Delta Nuttal store \$2.00 each, with fixed costs of \$1,000 per week for advertising.
(a) Use this data with that of Question 12 to give the weekly cost as a funtion of the unit price x they charge per CD.
(b) Use the results of part (a) and Question 12 to give the weekly profit in terms of the unit price x, and hence determine how much they should charge for maximum weekly profit.

Question 4 Sales of Gigantic State University Rugby Team memorabilia at the GSU bookstore for the months January-April were given by the following table:

 Month Jan. (t=0) Feb. (t=1) Mar. (t=2) Apr. (t=3) Sales (\$) 200 300 450 675

Which model is more appropriate: a linear model s(t) = mt + b or an exponential model s(t) = abt? Use your choice of models to predict sales in May.

Question 5 In airline industry terminology, one A.S.M. represents one passanger seat (whether sold or vacant) flown one mile. The following table shows Kiwi Airlines' growing capacity, measured in millions of A.S.M.s per month, for the period from February, 1994 through February, 1995.*

 Time Feb. 1994 (t = 0) Nov. 1994 (t = 0.75) Feb. 1995 (t = 1) Capacity(Million ASMs) 110 155 174.9

(a) Fit the data for February, 1994 and February, 1995 to an exponential model of the form

C(t) = Abt

for suitable constants A and b.

(b) How accurately does your model predict the November, 1994 figure?

(c) When, to the nearest quarter-year, does your model predict Kiwi's capacity as 400 A.S.M.s per month?

* The figures are rounded. Source: Company Reports/The New York Times, March 25, 1995, p. D5. 