If 2000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Question

Applied Optimization

If 2000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Volume = _____ cubic centimeters

Answer 1

2000 = x² + 4xy

2000 - x² = 4xy

(2000 - x²) / 4x = y

500 - (x / 4) = y

V = x²y

V = x²(500 - (x / 4))

V = 500x² - (x³ / 4)

Derive first derivative, set equal to zero, solve for x, and answer