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Maximizing Profits A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of...

Maximizing Profits

A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by

C(x) = 500 + 7x + 0.0003x2.

Each racket can be sold at a price of p dollars, where p is related to x by the demand equation

p = 10 − 0.0002x.

If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer. Hint: The revenue is

R(x) = px,

and the profit is

P(x) = R(x) − C(x).

rackets=

Math   Precalculus   
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