The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Minimizing the Cost of a Box

Date: 11/14/95 at 17:53:11
From: Anonymous
Subject: Business Calculus

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

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.