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
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