Question

An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible total area of the 4 pens?

Answer 1

let the width of one of the pens be x, let its length be y

so we have 8x + 5y = 720
y = (720 - 8x)/5 = 144 - 8x/5

area = 4xy
= 4x(144 - 8x/5)
= 576x - (32/5)x^2

d(area)/dx = 576 - 64x/5
= 0 for a max of area
64x/5 = 576
64x = 2880
x = 45

largest total area = 4(45)(144 - 8(45)/5)
= 12960 ft^2

check my arithmetic