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January 2nd, 2010, 08:23 AM  #1 
Newbie Joined: Jun 2008 Posts: 15 Thanks: 0  HELP w/ App. of Derivative Problem??? When cereal is shipped to the supermarket, it usually comes inside a bigger shipping box. Assume the total volume of the shipping box to be 25,000 cubic inches. Given:  the girth of each cereal box is mandated to be no larger than 20in.  height of each cereal box is fixed at 10in.  because height of cereal box will be 10in, 2 stacks of cereal boxes will fit in a shipping box  the shipping team wants to continue to fit 5 cereal boxes on the width  the shipping team wants to MINIMIZE the number of cereal boxes on the length  let "n" be the number of cereal boxes that can fit into a shipping box on the length How do I determine the WIDTH of a cereal box that MINIMIZES the number of cereal boxes that can be fit into a shipping box on the length? *** ANY OR ALL HELP APPRECIATED...thank you SO SO much... <33 
January 2nd, 2010, 05:17 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: HELP w/ App. of Derivative Problem??? Heloo, dagitt! Quote:
Each cereal box has length , width , and height Code: *     * / / / /  *      * 10         *   /  / y *      * x nx)(5y)(20) \:=\:100nxy \:=\:25,000 \qquad\qquad\Rightarrow\qquad\qquad n \:=\:\frac{250}{xy}" />[color=beige] .[/color][color=blue][1][/color] [color=beige]. . [/color][color=beige] .[/color][color=blue][2][/color] Substitute [color=blue][2][/color] into [color=blue][1][/color]: [color=beige]. . [/color] And that is the function we must minimize . . .Go for it!  

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