A manufacturer of athletic footwear finds that the sales of a popular brand of r

Question

A manufacturer of athletic footwear finds that the sales of a popular brand of running shoes is a function f(p) of the selling price p (in dollars) for a pair of shoes. Suppose that f(130) = 8500  pairs of shoes and f ' (130) = -60 pairs of shoes per dollar. The revenue that the manufacturer will receive for selling f(p) pairs of shoes at p dollars per pair is R(p) = (p) x [f(p)] Find R ' (130) What impact would a small increase in price have on the manufacturer's revenue?

Could someone help me figure out out to set up this problem?

Explanation / Answer

R(p) = (p) x [f(p)]

R'(p) = (p') x [f(p)] + p [f'(p)]

R'(130) = (1) x [f(130)] + 130*[f'(130)]

= (1) x [8500] + 130*[(-60)]

=8500 -7800

=700

small increase in price of 1 dollar after 130$ will increase in revenue worth 700pairs of shoes

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