Calulus

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Hi there I need help on my calculus homework and this week, we were working on partial derivative. I don't know how to approach this word problem and set it into a maximum or minimum. Well I am not too sure if this problem is a minimum or maximum problem. Please help me and this is the homework problem below

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 -

    Income=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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