Posted by **Heidi** on Friday, January 26, 2007 at 9:55pm.

A rectangular box with the volume 320 cu ft is built with a square base and a square top. The cost is $1.50/sg ft for the bottom, $2.50/sq ft for the sides and $1.00/sq ft for the top. Let x=the lenth of the base in feet. Express the cost of the box as a function of x. Where do I start?

You can see this better if you draw a rectangular box. The base is x and x so the area will be x^2.

The volume of the box is x^2 x height = x^2*h = 320 so solving for h we have

h=320/x^2.

Now figures the cost.

For the bottom the area is x^2.

The cost is 1.50/ft^2*(x^2) = ??

The cost of the top is

2.50/ft&2 *(x^2) = ??

The area of the sides is

h*x = (320/x^2)*x and the cost is that times 2.50/ft^2 and that times 2 (since there are two sides. Remember to put this cost in terms of x.

Then add all the costs.

Post your work if you get stuck.

Thx! I was making this harder than it needed to be! I originally got started like you said and thought it looked too easy!

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