A farmer has 1800 ft of fencing available to fence off a rectangular field bordering a straight river. no fence needed along the river. find the dimensions of the field that gives the maximum area. also, find the maximum area.
Let x be the width and y be the length of the rectangular area. The area is then given by the formula [tex]x\times y[/tex] We have the constraint 2x+y=1800. so y = 1800-2x. Therefore the are becomes in the following form: x(1800-2x). The above function has its max at x = 450 and the maximum area is 405000ft^2. The dimensions that gives the maximum area are the width x = 450 ft and the length y = 1800 - 450 = 1350 ft
