Question

A surfboard shop sells 45 surfboards per month when it charges $500 per surfboard. For each $20 decrease in price, the store sells 5 more surfboards per month. How much should the shop charge per surfboard in order to maximize monthly revenue?

Answer 1

Cost at which shop charge per surfboard in order to maximize monthly revenue is $300.

Step-by-step explanation:

Given : A surfboard shop sells 45 surfboards per month when it charges $500 per surfboard. For each $20 decrease in price, the store sells 5 more surfboards per month.

To find : How much should the shop charge per surfboard in order to maximize monthly revenue?

Solution :

A surfboard shop sells 45 surfboards per month,the store sells 5 more surfboards per month.

Let the surfboard sold be =
`45+5x`

It charges $500 per surfboard, for each $20 decrease in price.

The cost at which they will be selling surfboard will be
`500-20x`

Net revenue is

`(45+5x)(500-20x)=-100x^2+1600x+22500`

The maximum value of
`ax^2+bx+c` is when

`x=-(b)/(2a)`

Therefore, The maximum value of
`-100x^2+1600x+22500` is

`x=-(1600)/(2*(-100))`

`x=8`

Cost at which shop charge per surfboard in order to maximize monthly revenue is

Substitute the value of x in cost

`=500-20x`

`=500-20(8)`

`=500-160`

`=\$300`

Therefore, Cost at which shop charge per surfboard in order to maximize monthly revenue is $300.