• Support PF! Buy your school textbooks, materials and every day products Here!

Revenue Optimization problem

  • Thread starter jimen113
  • Start date
  • #1
67
0
[SOLVED] Optimization problem

Homework Statement


A baseball team plays in the stadium that holds 60000 spectators. With the ticket price at 8 the average attendence has been 24000. When the price dropped to 7, the average attendence rose to 30,000.
a) find the demand function p(x), where x is the number of spectators (assume p(x) is linear p(x)=
b) How should the ticket price be set to maximize revenue?


Homework Equations





The Attempt at a Solution


a) I figured out that the demand function was: 8-(1/6000)(x-24000)
b) I tried to use the revenue formula:; by taking the derivative of the demand function which is: 12-(12,000x/6000[tex]^{}2[/tex])
and then I set that equal to zero and tried to solve for X, which is: 36,000
So, now I don't know how to use the above information to calculate the price of the ticket. any suggestions?
 
Last edited:

Answers and Replies

  • #2
737
0
So x = 36,000 is a critical number of the revenue function [itex]r(x) = xp(x) = 12x - x^2 / 6000[/itex]. What does that tell you about r(x) at x = 36,000? What does that tell you about p(x)?
 
  • #3
67
0
I plugged in the x=36,000 into the demand function and I got $6.00 as the answer, I verified it and it is correct.
Thanks, I appreciate your help.
 

Related Threads for: Revenue Optimization problem

  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
6
Views
1K
Replies
1
Views
4K
  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
9
Views
3K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
7
Views
1K
Top