Question

A manufacturer has been selling hats at $8 a piece, and at this price, consumers have been buying 6000 hats per month. The manufacturer wishes to raise the price and estimates that for each $2 increase in the price, 500 fewer hats will be sold each month. The manufacturer can produce the hats at a cost of $4 per hat. At what price should the manufacturer sell the hats to generate the greatest profit? Explain your answer.

Answer 1

Answer:

$10

Step-by-step explanation:

Initial selling price per hat= $8

Number of hat sold= 6000

Revenue generated = $8*6000=$48000

Cost of producing hats = $4 per hat

Production cost = $4*6000=$24000

Profit = $48000-$24000=$24000

Increasing the price per hat by $2

Selling price per hat = $2+$8=$10

Number of hats sold are 500 fewer = 6000-500= 5500 hats

Revenue generated = $10*5500 = $55000

Cost of production is the same , where $4 per hat = $4*5500 =$22000

Profit generated = $55000-$22000 =$33000

This means at a price of $10 per hat , selling 500 fewer hats, the manufacture still makes a profit of $33000 which is $9000 more. It will be reasonable to hat at $10 because the profit will increase.