The University of Akron s7

The University of Akron Department of Mathematics

To: Calculus with Business Applications Students Date: Spring 2017 Subject: Project 1

Dear Calculus Students,

I am the owner of a manufacturing company which has recently introduced a new racket into the competitive market for tennis rackets. The rackets have been introduced in two cities. In one city the racket is priced at $50; at this price, 125 rackets are sold each week. In the second city the racket is priced at $45; 140 rackets are sold each week. (We can assume that the demand function p  f x for this racket is linear and that these two trial markets are reliable indicators of price and demand.)

Each week the company plans to produce at least 100 rackets at a fixed cost of $1400 and a variable x2 -100 x cost of for the production of x rackets, with x 100. I would like an analysis of the 12 relationship between costs, revenue and profit. In your analysis, please include the formulas for the demand function, cost function, revenue function and profit function with a clear explanation of how these functions were found. Find the number of rackets and price that maximize revenue and the number of rackets and price that maximize profit. Also find the maximum revenue and the maximum profit. Explain any difference in the price that maximizes revenue and the price that maximizes profit.

For this project, first work the problem algebraically, defining all of your variables, showing all of your work and giving an explanation of your steps.

Next using Excel, generate a table of values for the number of rackets, price, cost function, revenue function and profit function. Graph the cost function, revenue function, and profit function on a single graph. Your Excel chart should give a range of values to support your algebraic work. The maximum profit and maximum revenue should be clearly visible on your graph and in your table of values.

One type written report will be turned in by each group. Include in the report an explanation of how you found the necessary functions. You must show all of your calculations. Your solution needs to be clear, variables need to be defined and any equations used should be explained as clearly as possible.

Each member of the group must submit a typed evaluation of every other member of the group. This evaluation will be turned in separately by each member of the group.

Thank you very much for your help. I look forward to hearing from you soon.

Sincerely Yours, Someone Who Needs Your Help