Find the dimensions of the largest open-top storage bin with a square base and vertical sides that can be made from 108ft^2 of sheet steel. (Neglect the thickness of the steel and assume that there is no waste)

Answer 1

The volume is s^2 h
the surface area is s^2+ 4sh but

108=s^2+4sh
h=108/4s -s/4

put that into the volume equation for h, then take the derivative of V with respect to s, set to zero, and solve for s.

Answer 2

Thank you very much

Answer 3

What do you mean by with respect to zero?

Answer 4

He said set the derivative to zero to solve for the maximum.
Max or min when dV/ds = 0

Answer 5

Okay Thank You again

Answer 6

Excuse me the volume equation for this problem is V=s^2 h?

Answer 7

Yes, s^2, the side times the side, is the area of the base.
That times the height h is the volume of the box that you wish to maximize.

Answer 8

Okay but now I'm confused because when I find the derivative of the volume I get dv/dt=2s(ds/dt) then I don't know the rest because I have to find the derivative for 108/4s -s/4 which equals to h but what would be its derivative?

Answer 9

V=s^2 h= s^2 (108/s - s/4)
= 108s-s^3/4
dv/ds=0=108-3/4 s^2
now solve for s.
Once you get s, you can solve for h.

Answer 10

ooo okay Thank You