Optimization Problem:

Question

There is 300 square feet to construct an open top box with a square base. What dimensions are needed to maximize the volume, and prove that you have found the maximum

Answer 1

x^2 + 4xh = 300
v = x^2 h = x^2 (300-x^2)/4x
dv/dx = 5/4 x^2 (180-x)
max v is where dv/dx = 0, at x=√180