Asurfboard 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?

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 =

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

The cost at which they will be selling surfboard will be

Net revenue is

The maximum value of is when

Therefore, The maximum value of   is

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

Substitute the value of x in cost

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

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step-by-step explanation:

umm. i dont know

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)