word problem, help please?

Question

A company must manufacture a closed rectangular box with a square base. The volume must be 1160 cubic inches. The top and the bottom squares are made of a material that costs 5 dollars per square inch. The vertical sides are made of a different material that costs 2 dollars per sqare inch.
What is the minimal cost of a box of this type?

Answer 1

V = hs^2
A = 2s^2 + 4sh
C = 10s^2 + 8sh
h = V/s^2
C = 10s^2 + 8V/s
dC/ds = 20s - 8V/s^2 = 0 for max or min cost
20s = 8V/s^2
s^3 = 2V/5
s^3 = 2*1160/5
s ≈ 7.742 in.
h ≈ 19.354 in.
C = 10(7.742)^2 + 9280/7.742
C ≈ $1,798.04

check:
C = 10s^2 + 9280/s
C = 10(7.8)^2 + 9280/7.8 ≈ $1,798.14
C = 10(7.7)^2 + 9280/7.7 ≈ $1,798.09

Answer 2

Call the length and width x and height y. Then V = x^2 y = 1160 so y = 1160/x^2

The area of the top and bottom is x^2 each so 2x^2 (5) or 10x^2 is their cost. The area of the 4 sides is xy or x(1160/x^2) or 1160/x and there are 4 so their cost is
4(2)(1160/x)

So C = 8(1160)/x + 10x^2

Do this out then find its derivative and set it = 0 (if you are doing calculus)
If not, you could graph it.