Thursday

August 21, 2014

August 21, 2014

Posted by **shylo** on Sunday, October 25, 2009 at 11:55am.

A football stadium has a capacity of 50,000. The owners calculate that for an average game, if they charge $A for an adult ticket and $C for a child ticket, then N adults and M children will try to obtain tickets, where:

N = 80,000 - 2000A and

M = 30,000 - 1500C - 500A

Find the prices that the owners should charge in order to generate the maximum income from ticket sales for a game. (NOTE: It may not be necessary for the stadium to be full to maximum income.)

- Calulus -
**bobpursley**, Sunday, October 25, 2009 at 2:15pmIncome=A*N + C*M

=A(80000-2000A)+C(30000-1500C-500A)

multiply it out

Take derivitive with respect to A or C, I will do C first:

dI/dc=30000-3000C set it to zero, then

C=10

Now, do dI/dA

80000-4000A -500C=0

or A=80000-5000)/4000=75/4=17 dollars

Check: make certain the stadium can hold N +M

N=46000 M=6500 so yes it can.

check this.

**Related Questions**

Calulus - Hi there I need help with one of the problem from my homework package...

calculus - Find the surface area of the part of the sphere x^2+y^2+z^2=a^2 ...

Calculus - Hi there I am having some troubles trying to do my calculus homework ...

Math subject Calculus - Hi there I am having some difficulties to solve this ...

Partial derivative - Hello I trying to do a problem on partial derivative. I ...

math/algebra - Can I get help in solving these problems using the linear system ...

Calculus - Integration - I came across this problem in my homework, and I was ...

Calc - Classify all critical points of the function f(x,y)=x^2-y^2+4x-2y+1. I ...

Calculus (Help) - Also I would like to know how to set this problem up in ...

Calculus - I've been working on this problem for while, and I keep getting the ...