At a price of $7.5 per ticket, a musical theater group can fill every seat in their 1500 seat performance hall. For every additional dollar charged for admission, the number of tickets sold drops by 95.

Question

a) What ticket price maximizes revenue? Round your answer to the nearest cent.
price = $ 885/76

b) How many seats are sold at that price? Round your answer to the nearest whole number.
number of seats sold =

I got part a, but when I plug that number back into the revenue equation it does not give the right answer to b. How do you solve problem b?

Answer 1

Problem b is a little tricky but I can help.
You found the price at 11.64. Use this.
This just requires some thought.

11.64-7.5=4.14 <-the amount of price increase
4.14*95 <- how many people will not attend now

Subtract how many will not attend now from max and there you go!
Good luck. :)

Answer 2

let the number of additional dollars be x

new price = 7.5+x
number of tickets sold = 1500 - 95x

Revenue = (7.5 + x)(1500-95x)
= 14250 + 787.5x - 95x^2
d(Revenue)/dx = 787.5 - 190x
= 0 for a max of Revenue
190x = 787.5
x = 4.14
ticket price = 7.5+4.14 = $11.64
number of tickets = 1500-95(4.14) = 1106.25
but you cant' sell a partial ticket
number sold = 1106