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

Mathematics

Brenda Ball

7 September, 00:47

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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Bush · 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