A farmer has 2200 feet of fencing available to enclose a rec

A farmer has 2200 feet of fencing available to enclose a rectangular area bordering a river. If no fencing is required along the river, find the dimensions of the fence that will maximize the area. What is the maximum area? Find the dimensions of the fence that will maximize the area. Width = feet Length = feet The maximum area is square feet.

Solution

Let length of fence be l and width be w

Total length of Fence : l +2w = 2200

Area = l*w = (2200 -2w)w = -2w^2 +2200w

Maximum area is achieved at the vertex of the quadratic equation:

ax^2 +bx +c =0 ---> x= -b/2a

w = -(2200)/(2*-2) = 2200/4 = 550 feet

width : w= 550 ft

length : l =2200 -2w = 1100 ft

maximum area = 550*1100 = 605000 ft^2