How many pairs of socks must be sold to yield a maximum revenue? What will the maximum revenue be? (Round your answer to the nearest cent.)

Question

Maximizing Revenue

 The unit selling price p (in dollars) and the quantity demanded x (in pairs) of a certain brand of men's socks is given by the demand equation

p=14e^-0.0008x  (0 ≤ x ≤ 10,000)

Answer 1

Revenue R(x) = px = 14xe^{- 0.0008x} (0 ≤ x ≤ 10000)

R'(x) = 14e^{- 0.0008x}- 0.0112xe^{- 0.0008x} = 0; 14 - 0.0112x = 0; x = 14/0.0112 = 1250.

This is maximum because left from 1250 R'(x ) > 0 and right from 1250 R'(x) < 0

R_max = R(1250) = 14·1250·e^{- 1} = $6437,89