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?

Question

Larry

Mathematics

2 June, 00:03

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?

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Answers (1)

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Sophia · 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