Chapter R.4, Problem 67E

Profit-and-loss analysis. Red Tide is planning a new line of skis. For the first year, the fixed costs for setting up production are $45,000. The variable costs for producing each pair of skis are estimated at $80, and the selling price will be $450 per pair. It is projected that 3000 pairs will sell the first year.

a. Find and graph $C\left(x\right)$, the total cost of producing x pairs of skis.

b. Find and graph $R\left(x\right)$

the total revenue from the sale of x pairs of skis Use the same axes as in part (a).

c. Using the same axes as in part (a), find and graph $P\left(x\right)$, the total profit from the production and sale of x pairs of skis.

d. What profit or loss will the company realize if the expected sale of 3000 pairs occurs?

e. How many pairs must the company sell in order to break even?