My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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
dagitt is offline  
 
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:
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.
- - The 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?

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!

soroban is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
app, derivative, problem, w or



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Derivative Problem KMT Calculus 1 September 25th, 2011 07:55 PM
Derivative problem azelio Algebra 2 October 17th, 2010 06:24 PM
HELP w/ App. of Derivative Problem??? dagitt Calculus 3 January 5th, 2010 09:30 PM
Derivative Problem tomotomo Calculus 3 February 16th, 2009 05:18 PM
Problem with derivative StevenMx Calculus 6 February 4th, 2009 08:14 AM





Copyright © 2018 My Math Forum. All rights reserved.