Maximize Revenue

Question

A fitness club sells its memberships at a fee of $100/month. The club sells 30 memberships per month. CEO of this club estimates that every $10 discount in membership fee, number of users will increase by 6 each month. What price should the memberships be sold for in order to maximize revenue?

Answer 1

(0, 150)

(30,100)

(36, 90)

(90, 0)

graph the line through the points. The midpoint is the revenue maximizing price and quantity of membership sold

midpoint is (45, 75) $75 monthly charge and 45 memberships are sold

for maximum revenue = 45(75) =225 +3150 = $3375

or find the equation of the line through the points

slope = -5/3 = (y-100)/(x-30)

y-100 = -5x/3 +50

y or P(x) = -5x/3 +150

Revenue = R = Px = -5x^2/3 +150x

R' = -10x/3 +150 = 0

x = 150(3/10) = 45

P= -5(45)/3 + 50 = 75