Calulus
posted by shylo on .
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.)

Income=A*N + C*M
=A(800002000A)+C(300001500C500A)
multiply it out
Take derivitive with respect to A or C, I will do C first:
dI/dc=300003000C set it to zero, then
C=10
Now, do dI/dA
800004000A 500C=0
or A=800005000)/4000=75/4=17 dollars
Check: make certain the stadium can hold N +M
N=46000 M=6500 so yes it can.
check this.