Question

A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence?

Answer 1

  13.5 = lw 

13.5/l = w 

3l + 2w = C 

C = 3l + 2*(13.5/l) 

C = 3l + (27/l) 

dC(l)/dl = 0 

3 - (27/l^2) = 0 

3*(l^2) - 27 = 0 

(l^2) - 9 = 0 

(l - 3)*(l + 3) = 0 

l = 3 

13.5 = 3w 

l = 3000; w = 4500

Therefore, to minimize the cost of the fence, length should be 3000 ft while width should be 4500 ft.