A rancher wants to build a rectangular fence next to a river, using 100 yd of fencing. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the rancher should not fence the side next to the river.)

Answer 1

If the length (parallel to the river) is y,

2x+y = 100
a = xy = x(100-2x) = 100x-2x^2
max a at x = 100/4 = 25

So, the yard is 25x50

As usual, max area when the fence is divided equally among lengths and widths.