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Bob wants to create two pens, as shown in the figure. One pen if for a garden and it needs a heavy duty fence to keep out the critters. This heavy duty fence costs $24 per foot. The dog pen shares a side with the garden and has a lighter weight fence on the other three sides that costs $6 per foot. If each pen is to have an area of 1,440, find the values of x and y that would minimize the total cost of the fencing.

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Below is the solution:

30x+10x+5y+30y = 40x +35y
which means your cost function is C(x) = 40x+17640/x
then taking the derivative C'(x) = 40-17640x^-2
set that equal to zero and solve
x=21
so 504 = 21y
y =24

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