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Math87
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Homework Statement
A corporation manufactures candles at two locations. The cost of producing x1 units at location 1 is C1= 0.02X12+4X1+500
and the cost of producing x2 units at location 2 is C2=0.05X22+4X2+275.
The candles sell for $15 dollars per unit. Find the quantity that should be produced at each location to maximize the profit.
p=15(X1+X2)-C1-C2
The Attempt at a Solution
First off, my professor said "This is just for convenience, especially when plotting it in wolfram alpha, you can't enter x1 and x2 but you can enter x and y. So in the give equations, change the letters, making x1 into x and make x2 into y. Then you will have an equation with numbers and x and y ."
i changed everything to x and y
C1= 0.02X2+4X+500
C2= 0.05Y2+4Y+275
Then i decided to combine them together to get:
0.02X2+4X+500-0.05y2-4Y-275=0
After that i found my 6 partial derivatives, but i have a feeling I am doing this all wrong..
Can you give me tips on how to do this question please.