Cost, Revenue and Profit Functions and Break-Even Points

3. Antonio would like to invest $5,000. He has the choice of two accounts, one that pays 2.3% compounded continuously or the other that pays 2.5% compounded quarterly. Which account would yield the higher return?

4. A manufacturer of tennis shoes is planning a new line of shoes. For the first year, the fixed costs for setting up the new production line are $28,500. The variable cost for producing each pair of shoes are estimated at $50. The sales department projects that the shoes can be sold during the first year at a price of $95 per pair.

a. Formulate the cost function, the revenue function, and the profit function. Let x represent the number of pairs of shoes produced and sold.

C(x) =

R(x) =

P(x) =

b. What profit or loss will the company realize if 30,000 pairs of shoes are sold?

c. Find the number of pairs of shoes the company needs to produce and sell in order to break even.

d. If the company sells 100,000 pairs of shoes during the first year, compute the average cost of each pair of shoes.

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