Question

A farmer is fencing a rectangular area for his farm using the straight portion of a river as one side of the rectangle. If the farmer has 2400 ft of fence, find the dimension of the rectangle that gives the maximum area for the farm

Answer 1

So we need 2 widths and 1 length
let the width be x
and the length be y
2x + y = 2400
y = 2400-2x

Area = A = xy
= x(2400-2x)
= 2400x - 2x^2

dA/dx = 2400 - 4x = 0 for a max of A
4x = 2400
x = 600
then y = 2400-1200 = 1200

field is 600 ft by 1200 ft