Mr. parker's farm borders a river. he buys 1,000 ft of fencing a) what dimensions maximize the area of the farm? b) what is the maximum area of the farm?

When one side of a quadrilateral is not to be fenced (ex. a river, as in this case), the optimal fencing to maximize the area is always to use half the fencing for the length, and one-fourth for each of the two widths

A) For 1000 ft of fencing which is to be used to cover 1 length and 2 widths:
L = 1000/2 = 500, and W = 1000/4 = 250. The optimal dimensions will be 250 x 500 ft.

B) This will result in an area of 250*500 = 125,000 sq. ft.