Question

Optimization:

Answer 1

If \(1,200 cm^2\) of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answer 2

Let x be length and width, h be height

SA = x^2 + 4hx = 1200

--> h = (1200 -x^2)/4x

V = hx^2 = 300x - x^3/4

maximize volume by setting derivative equal to 0
dV/dx = 300 - 3x^2/4 = 0

--> x = 20

--> max V = 4000

Answer 3

Thank you :)

Answer 4

yw :)