A health club currently charges its 1500 clients monthly membership dues of $ 44. The board of directors decides to increase the monthly membership dues. Market research shows that each $ 1 increase in dues will result in the loss of 5 clients. How much should the club charge each month to optimize the revenue from monthly​ dues?

Accepted Solution

Answer:The club should charge $172 to optimize the revenue.Step-by-step explanation:Hi there!The revenue can be calculated as the number of clients times the value of the membership dues. Let y be the revenue, then:y = 1500 · 44Let x be the increase in membership dues, then for a increse of x, the number of clients lost will be 5x:y = (1500 - 5x)(44 + x)y = 66000 - 220x + 1500x - 5x²y = -5x² + 1280x + 66000It is a quadratic equation, a negative parabola. The maximum is the vertex of the parabola that is calculated as:x = -b/2aWhere:b = 1280a = -5 Then:x = -1280/2 · (-5)x = 128The club should charge 44 + 128 = $172 to optimize the revenue.