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### Minimizing the Cost of a Box

```
Date: 11/14/95 at 17:53:11
From: Anonymous

A closed box with a square base is to contain 252 cubic feet.
The bottom costs \$5 per square foot, the top costs \$2 per square foot,
and the sides cost \$3 per square foot.  Find the dimensions that will
minimize the cost.
```

```
Date: 12/7/95 at 6:3:3
From: Doctor Jonathan
Subject: Re: Business Calculus

When you want to minimize a function, you find the points where that
function's first derivative is zero.  This will either be a maximum
or a minimum.  To determine which, you need only look at the sign of the
second derivative at that point; if it's positive you have a minimum, if
negative, a maximum. I have a feeling your problem will require the
minimization of a function of two variables, but the same principles
apply (replace deriv. with gradient). If you need further help, please
feel free to write back.

-Doctor Jonathan,  The Geometry Forum

```
Associated Topics:
High School Calculus

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