Optimization problem

Question

I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $8 per foot, and the fencing for the east and west sides costs $4 per foot. If I have a budget of $240for the project, what are the dimensions of the garden with the largest area I can enclose?

Answer 1

x+y=30

A=xy=x(30-x)

A'=0=30-2x

x=15,y=15

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