A divided field is to be constructed with 4160 feet of fen00

A divided field is to be constructed with 4160 feet of fen0063e as shown. For what values of x and y will the area be a maximum?

Solution

The perimeter of fence you need is 2x+4y=4160. The area is xy=A. Thusly, x=2080-2y A=(2080-2y)*y Here, I like to apply product rule rather than multiply through and use power rule. dA/dy=(2080-2y)+y*(-2)=0, because extreme values occur where the derivative =0. 2080=4y y=520 Then x=2080-2(520)= 1040 The question is entirely answered, but as a check: 2*(1040)+4*(520)=4160, good. And the maximum area is 1040*520=540,800.