zachutnat4o

2021-11-14

At HD Sport and Fitness gym, analysis shows that, as the demand of the gym, the number of members is 86 when annual membership fee is $25 per member and the number of members is 84 when annual membership fee is$33 per member. As the operator of the gym, you found out that number of members (q) and membership fee (p) have a linear relationship.
A) At what membership price, p , is the revenue maximized?
$p=$
B) What is the maximum annual revenue?
$R=$.

breisgaoyz

We find for (a)
$R\left(p\right)=\frac{-5}{2}+240p$
$\frac{-5}{2}\cdot {\left(86\right)}^{2}+240p$
$\frac{-5}{2}\cdot 7396+240$
We find for (b)
$R=\left(q\right)=\frac{2}{5}\cdot {q}^{2}+96p$
$=\frac{2}{5}\cdot {\left(84\right)}^{2}+96q$
$\frac{2}{5}\cdot 7056+96q$

Do you have a similar question?