Optimization Problem: Minimizing rectangle dimensions

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SUMMARY

The forum discussion centers on the optimization problem of determining the minimum dimensions of a rectangular enclosure given a specified volume of 144 cubic meters. Participants emphasize the importance of understanding the relationship between volume and dimensions, specifically using the formula for volume (length × width × height). A key point raised is the necessity for the user to clarify the volume measurement, as it was incorrectly stated in square meters instead of cubic meters. The discussion highlights the need for a systematic approach to solving optimization problems in calculus.

PREREQUISITES
  • Understanding of calculus concepts, particularly optimization techniques.
  • Familiarity with the formula for calculating the volume of a rectangular prism.
  • Basic knowledge of vectors and their applications in geometry.
  • Ability to interpret and correct measurement units in mathematical problems.
NEXT STEPS
  • Study optimization techniques in calculus, focusing on critical points and constraints.
  • Learn how to derive and apply the volume formula for three-dimensional shapes.
  • Explore methods for solving real-world problems involving dimensions and volume.
  • Practice correcting and interpreting measurement units in mathematical contexts.
USEFUL FOR

High school students studying calculus, educators teaching optimization problems, and anyone interested in applying mathematical concepts to real-world scenarios involving volume and dimensions.

Kenny Bala
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Hi guys, I'm a high school senior currently in calculus and vectors. We're in our application unit right now, and I'm having quite a bit of trouble with problems that give the desired volume/area, and then ask you for the minimum dimensions required for said volume. One notable problem that I am unable to figure out can be seen here: http://prntscr.com/6qcz7c

Could you guys give feedback on the problem and if possible, explain a general method of determining minimum dimensions? I can work with having dimensions given to me, but not with volume given instead.
 
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Sorry, Kenny, according to the Rules at PF, we can only offer assistance to those who make an attempt at solving their problems first.

You should make your best attempt, show us what you've done, and tell us where you are getting stuck.

Your problem states that the enclosure has a volume of 144 m2, which must be a typo, since volume is measured in cubic meters.

It's not clear why you can't work with a stated volume. Don't you know how to calculate the volume of a rectangular enclosure using the length, width and height?
 

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