Question

I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $176 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose?

Answer 1

x = E/W dimension
y = N/S dimension

4x + 4x + 2y + 2y = 64
8x + 4y = 64
4y = 64 - 8x
y = 16 - 2x

Area = xy = x(16 - 2x) = 16x - 2x^2

Maximum of y = ax^2 + bx + c is when x = -b / 2a

so x = -16 / -4 = 4