Question

If 1500 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 =

Answer 1

let the base be x cm by x cm, and the height y cm

then x^2 + 4xy = 1500
y = (1500 - x^2)/(4x)

V = x^2y
= x^2(1500 - x^2)/(4x)

expand, find dV/dx
set that equal to zero and solve

let me know how you made out.