Question

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

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