Respuesta :
Answer:
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 = [tex]45+5x[/tex]
It charges $500 per surfboard, for each $20 decrease in price.
The cost at which they will be selling surfboard will be [tex]500-20x[/tex]
Net revenue is
[tex](45+5x)(500-20x)=-100x^2+1600x+22500[/tex]
The maximum value of [tex]ax^2+bx+c[/tex] is when
[tex]x=-\frac{b}{2a}[/tex]
Therefore, The maximum value of [tex]-100x^2+1600x+22500[/tex] is
[tex]x=-\frac{1600}{2\times(-100)}[/tex]
[tex]x=8[/tex]
Cost at which shop charge per surfboard in order to maximize monthly revenue is
Substitute the value of x in cost
[tex]=500-20x[/tex]
[tex]=500-20(8)[/tex]
[tex]=500-160[/tex]
[tex]=\$300[/tex]
Therefore, Cost at which shop charge per surfboard in order to maximize monthly revenue is $300.
