fence length = x = 4w + 2L
L w = 75000 so L = 75000/w
x = 4 w + 150,000/w
dx/dw = 0 for max or min x
0 = 4 -150,000/w^2
w^2 = 150,000/4
w^2 = 37500
w = 193.6
x = 4 w + 150,000/w
x = 4(193.6) + 150,000/193.6
x = 1549 meters
A landowner wants to fence in a rectangular area of 75000 square metres and divide it into three parts with two parallel fences both parallel to one side of the rectangle. Each part will have a different grazing crop for the herds. What is the shortest total length of fence that he can use in metres?
1 answer
1 answer