The marketing department of a local shoe company found that approximately 600 pairs of running shoes are sold monthly when the price of each pair is $90. It was also observed that, for each $1 reduction in price, an additional 20 pairs of running shoes are sold monthly. What price should the shoe store charge for a pair of running shoes in order to maximize revenue?

Question

Darnell Ramsey

Business

20 July, 19:19

The marketing department of a local shoe company found that approximately 600 pairs of running shoes are sold monthly when the price of each pair is $90. It was also observed that, for each $1 reduction in price, an additional 20 pairs of running shoes are sold monthly. What price should the shoe store charge for a pair of running shoes in order to maximize revenue?

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Jefferson · Answer 1

The price should the shoe store charge for a pair of running shoes in order to maximize revenue is $60

Explanation:

Denot x is the amount of dollar reduction in sell price made in comparison to the original selling price of $90. Thus, we have:

New selling price = (90-x); New quantity sold = (600 + 20x)

We have the equation for revenue denoted as y after price reduction is:

y = (90 - x) x (600 + 20x) y = - 20 x^2 + 1,200x + 54,000

Thus, revenue is described by quadratic equation and will be maximize at the reduction price of $x result in y that is the maximum value of a parabola. As a result x = - 1,200 / 2 x (-20) = $30

Thus, selling price to maximize revenue = 90 - 30 = $60.