Answer:
The club should charge $211 to optimize the revenue.
Step-by-step explanation:
Hi there!
The current revenue of the health club is calculated by multiplying the number of clients by the membership due value.
If y = revenue, then:
y = 1900 · 42
So, if the memberiship dues increase by $1, 5 clients will be lost. Then, if the dues increase by a value of x, then the number of lost clients will be 5x. If such an increase is applied, the revenue will be:
y = (1900 - 5x) (42 + x)
Apply distributive property:
y = 79800 + 1900x - 210x - 5x²
y = -5x² + 1690x + 79800
The function is a negative parabola, then, its maximum will be the vertex of the parabola that can be calculated using the following formula:
x = -b/2a
Where:
b = 1690
a = -5
Then:
x = -1690/(2 · -5)
x = 169
The club should charge 169 + 42 = $211 to optimize the revenue.
