SOLUTION: An open-top box with a square base is to be made from two materials, one for the bottom and one for the sides. The volume of a box is to be 18 cubic feet. The cost of material for

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Question 1086801: An open-top box with a square base is to be made from two materials, one for the bottom and one for the sides. The volume of a box is to be 18 cubic feet. The cost of material for the bottom is P10.00 per square foot and the cost of the material for the sides is P7.00 per square foot. determine a model for the cost of the box as a function of its height h. what is the domain of the function?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An open-top box with a square base is to be made from two materials, one for the bottom and one for the sides.
let s = the side of the square base
let h = the height of the box
The volume of a box is to be 18 cubic feet.
s * s * h = 18
s^2 * h = 18
s^2 = 18%2Fh
s = sqrt%2818%2Fh%29
The cost of material for the bottom is P10.00 per square foot and the cost of the material for the sides is P7.00 per square foot
Surface area:
S.A. = s^2 + 4(s*h)
Cost = 10s^2 + 7(4s*h)
C = 10s^2 + 28s*h
determine a model for the cost of the box as a function of its height h.
Replace s with sqrt%2818%2Fh%29
C(h) = 10sqrt%2818%2Fh%29%29%5E2 + 28*sqrt%2818%2Fh%29*h
C(h) = 10(18%2Fh) + 28*sqrt%2818%2Fh%29*h
simplify, extract the square root of 9
C(h) = 10(18%2Fh) + 28*3sqrt%282%2Fh%29*h
C(h) = 180%2Fh + 84sqrt%282%2Fh%29*h
:
what is the domain of the function,
all positive values for h
:
:
Looks like this, y = Cost; x = height

minimum cost when height = 2, the side of the square base = 3
That would be 10(3^2) + 7(4*2*3) = $258