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July 25, 2014

July 25, 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.

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