Probability

Question

A shoe retailer finds that she can sell 20 pairs per month of a certain model when the price is $43 per pair and that for each dollar by which she lowers the price, her monthly sales increase by 4 pairs. If the shoes cost her $29 a pair wholesale, which of the following gives a correct expression for her monthly profit $P in terms of her selling price $x per pair

Answer 1

Let x be her selling price and x ≤ 43.  Then 43 - x would be the dollar decrease in the price of a pair of shoes.

 

The sales S would be S = (20 +4(43 - x))*x, since for each dollar decrease in price 4 more pairs of shoes are sold.

S = (192 - 4x)*x

The cost would C = 29 * (192 - 4x)

 

The profit would be P = S - C = (192 - 4x)*x - 29 * (192 - 4x)

                               = (192 - 4x)(x - 29)

                               = -4x² + 308x - 5568