SOLUTION: Hi. I don't know how to set up this problem, let alone solve it. Thanks in advance. A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a squ

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Question 703612: Hi. I don't know how to set up this problem, let alone solve it. Thanks in advance.
A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. Express the surface area A of the box in terms of the width w of the base. If the material for the base and top costs 30 dollars/ft^2 and that for the sides costs 40 dollars/ft^2 express the total cost C as a function of the width.
A(w)= _________ ft^2
C(w)= _________ $
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Here's help for the surface area.
I'm using variable name x instead of w..., x is for width.
Square base,using x as the length of side of base, means x by x area. Using h as height, then volume is 2=x*x*h.

Total surface area counting only one side of each piece:
x^2 + x^2 for top and bottom,
4*x*h for all of the sides,
Area A=2x^2+4xh
Using volume relationship and h=2/x^2,
Area
OR

Finding the cost, the is the more sensible formula to use. The first term represents the top and bottom; and the second term represents the side.