A farmer has 1000 feet of fencing materials available to fence a rectangular pasture next to a river. If the side along the river does not need to be fenced, what dimensions maximize the enclosed area? What is the maximum enclosed area?

Answer 1

let side parallel to river be y
let the other two sides be x each

2x + y = 1000 , ----> y = 1000-2x

area = xy = x(1000-2x) = 1000x - 2x^2

if you know Calculus.....
d(area)/dx = 1000 - 4x
= 0 for a max of area
4x =1000
x = 250
y = 1000-2(250) = 500

so max area = xy = 250(500) = 125000 ft^2