maximize revenue and atendance.

Question

Patty is organizing a school dance for student council. At last year’s dance, they charged $10 per ticket and they sold 94 tickets. Looking at records from previous years, Patty estimates that for every $1 increase, 5 fewer students will attend. What price will maximize their revenue? How many students will attend?

Answer 1

student tickets sold = X = -5P + 144

-5P =X-144

Price = P = (-1/5)X + 144/5 = -X/5 + 28.8

Revenue = R = PX = -X^2/5 + 28.8X

R' = -2X/5 + 28.8= 0

2X/5 = 28.8

X = (5/2)28.8 = 5(14.4) = 72 students will attend

P = -(1/5)72 +28.8 = 28.8-14.4 = $14.40 = profit maximizing price

maximum profit = 72(14.4) = $1,036.80