Question

A rancher has 600 ft of fencing to enclose three adjacent rectangular corrals. Write the total area as a function of x.

Answer 1

A(x) = -2X² + 600X

Explanation:

Area = X · Y

Perimeter = 2X + Y = 600

Y = 600 - 2X

A(x) = X · (600 - 2X) = 600X - 2X²

A(x) = -2X² + 600X

if you want to maximize area:

A'(x) = -4X + 600 = 0

600 = 4X

X = 150

Y = 600 - (2 · 150) = 600 - 300 = 300

Area = 150 · 300 = 45,000 ft²