SOLUTION: A closed box is to be a rectangular solid with a square base and a volume of 12 cubic feet. Find the most economical dimensions if the top of the box is twice as expensive as the s

Question 241084: A closed box is to be a rectangular solid with a square base and a volume of 12 cubic feet. Find the most economical dimensions if the top of the box is twice as expensive as the sides and the bottom?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A closed box is to be a rectangular solid with a square base and a volume of 12 cubic feet.
Find the most economical dimensions if the top of the box is twice as expensive as the sides and the bottom?
:
Let dimension of the square bottom = x, area of the bottom and top = x^2
volume
let h = the height of the box
x^2 * h = 12
h =
:
Surface area,
Since the top cost twice as much as the bottom, we can treat them like 3x^2 instead of 2x^2,
:
S.A. = 3x^2 + 4(x*h)
Replace h with
SA = 3x^2 + 4x*
Cancel an x
SA = 3x^2 +
:
Plot this equation

:
Minimum surface area is minimum expense, occurs when x = 2 inches
:
Find h:
h =
h =
h = 3 inches
:
2 by 2 by 3 is the dimensions of the box
:
You can see that if the top and bottom cost the same we would have
2x^2 + and the graph would be:

about x = 2.25 inches
:
:
HOpe this made sense to you
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