A small corral is to be built, to split it into 2 smaller areas with fencing to separate the animals.There is 60m of fencing available to build the corral,what's the maximum area that can be enclosed?

Answer 1

60 = 2L + 3W

2L = 60-3W

L = 30 -3W/2

Area = A = LW = (30-3W/2)W = 30W - (3/2)W^2

take the derivative, set it equal to zero and solve for W for maximum area

A' =30 -3W =0

3W=30

W=30/3 = 10 meters

L= 30- (3/2)10 = 30-15= 15 meters

That's 2 smaller areas of 75 square meters each, 7.5 m x 10 m

max Area = 10x15 = 150 square meters