You are asked to design a rectangular box with a square bottom with total volume $V$=11 cubic feet. The material:

  • $2.75 per square foot for the base of the box

  • $2.50 per square foot for the sides of the box

  • $0.50 per square foot for the top of the box

What should the height be to minimize the cost of material.

I'm stuck on this problem. I keep following the example that is given in my textbook but for some reason my answer is too high.

Can anybody please help me solve it????


1 Answer 1


Here are some hints: You're trying to minimize the cost of building the box. Your box has a square base, say of side length $s$. Call the height of the box $h$. Using what you know, you can express the cost of the box as a function of $s$ and $h$. How?

You should now have a cost function $C(s,h)$ that you wish to minimize. To do this, you need to find a way to express $C(s,h)$ as a function of a single variable. Since they're asking about the height for which the cost is minimized, ideally you'll find a way to rewrite $C(s,h)$ as a function $f(h)$ of the height.

How can you do this? What information about the box have you not used yet? Find a way to use this information to express $s$ in terms of $h$. This will allow you to rewrite $C(s,h)$ solely in terms of $h$.


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