let the base be x by x cm
let the height be y
given: 4x + y = 120
y = 120 - 4x
V = x^2 y = x^2(120-4x)
= 120x^2 - 4x^3
dV/dx = 240x - 12x^2 = 0 for a max of V
12x^2 - 240x = 0
12x(x- 20) = 0
x = 0 ----> yields a minimum volume
or
x = 20
so the box is 20 cm by 20 cm by 40 cm for a max volume of 16000 cm^3
A box has a Square base. The Perimeter of the base plus the height is 120cm. What is the max volume of this box, and what are the dimensions of the this maximized box.
1 answer