Jim wants to build a rectangular parking lot along a busy street but only has 3,000 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot

Question

Milton Sexton

Mathematics

12 February, 15:30

Jim wants to build a rectangular parking lot along a busy street but only has 3,000 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot

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Answers (1)

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Jacey Yang · Answer 1

Let x be the length of a side of the fence that is perpendicular to the street. Then the length of side at the back of the lot parallel to the street is 1000 - 2x.

So we want op maximize x * (1000-2x) = - 2x^2 + 1000x.

If you're not using calculus set up a spreadsheet where you very x from 0 to 500, calculating the area for each x.

If you are using calculus then the derivative of - 2x^2 + 1000x is - 4x + 1000 which is 0 when x = 250 which is when the ara will be maximum. Plugging in x=250 in the original equation gives us 250*500 = 125000 sf