posted by Heidi on .
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
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!