Minimizing Material Used for a Box

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Discussion Overview

The discussion revolves around a problem set involving the optimization of a box's dimensions to minimize material usage, specifically focusing on a box without a top. Participants are examining the surface area and volume formulas, as well as the steps to derive the necessary dimensions.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a formula for surface area (SA) and volume, suggesting a calculated length and height for the box.
  • Another participant challenges the correctness of the calculated length and requests the original steps to verify the solution.
  • A third participant reiterates the request for steps and provides their own expression for the derivative of the surface area, proposing a different approach to find the length.
  • There is a confirmation from one participant that the derivative provided is correct, prompting further inquiry about the resulting length.

Areas of Agreement / Disagreement

There is disagreement regarding the correctness of the calculated length, with multiple participants offering different approaches to derive the solution. The discussion remains unresolved as participants seek clarification and verification of steps.

Contextual Notes

Participants have not reached consensus on the correct length, and there are unresolved mathematical steps regarding the optimization process.

ardentmed
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Hey guys,

I'm having trouble with this problem set I'm working on at the moment. I'd appreciate some help with this question:

(I'm only asking about number two, not one. Thanks.)
08b1167bae0c33982682_23.jpg


The lack of a top is accounted for in the formula for the box's surface area, which should be:

SA= L^2 +4HL
And the volume is simply:
32,000 = HL^2

THerefore, solving for the derivative of SA (or dSA) should give:

3L^2 - L^3 - 12,800.
L = 18.56635.

Ergo,
h=92.831.

Therefore, the dimension should be:
18.6cm x 92.8cm x 18.6cm

Am I close? Are the significant figures off?
Thanks in advance.
 
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The length you got is wrong. Can you show me the your steps?

$$SA (l) = l^2 + \frac{4(32000)}{l}$$

Take its derivative and tell me what you get.
 
Last edited:
Rido12 said:
The length you got is wrong. Can you show me the your steps?

$$SA (l) = l^2 + \frac{4(32000)}{l}$$

Take its derivative and tell me what you get.

I believe that the derivative is:

dSA = 2l - 128,000/(l^2)

Multiply the expression by the common denominator and solve for l.

Am I on the right track? What do I do from here?
 
Yes, that is right. What do you get for the length?
 

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