Question

A farmer with 700 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens.

Answer 1

Note that the rectangular area divided into four pens with fencing parallel to one side of the rectangle as shown x y Label it in different color to form the constraint equation X y The constraint is, 2x 5y 700 This gives us [Here x 's in blue and y 's in green] 700 2x y = 5 It is need to maximize the total area

Area of the rectangle is, A=xy 700-2x 5 2 x +140x 5 2 x 140x 5 Thus, A(x) 4 A'(x)x+140 5 4 x140 0 5 A'(x) 0 implies 4 -x=-140 5 4x 700 x = 175 And 4 <0 A'(x) 5 Nn

Therefore, the area has maximum value at x =175 And the maximum possible area is, 2 x +140x 5 A(175)(175) +(140) (175) use x 175 in A(x)- 2 12, 250 sq ft