Quadratic functions

Question

Helmut, the ostrich farmer wants to build a rectangular fenced enclosure divided into five rectangular pens. A total length of 120M (meters) of fencing material is available. Find the overall dimensions of the enclosure that will make the total area a maximum

Answer 1

120 meters total

for 5 rectangular adjoining pens

x = one side of each of the 5 pens

(120-5x)/2 = 60-2.5x = length of each of the other 2 perpendicular sides

total area = A(x) = 60x -2.5x^2

A'(x) = 60-5x = 0

x = 60/5 = 12 meters

other 2 sides are 60-2.5(12) = 30 meters

max A = 12(30 = 360 m^2