You have 300 square feet of wood you will use to construct a rectangular shed with a square base and top. What is the maximum volume of your shed? Optimization Question

Answer 1

base side x
height y
2x^2+4xy = 300 ==> y = (300-2x^2)/(4x)

v = x^2y = x^2(300-2x^2)/(4x) = 75x - x^3/2
dv/dx = 75 - 3x^2
dv/dx=0 at x=5

So, the shed is 5x5x12.5, with v=312.5 ft^3