anonymous
  • anonymous
Restriction help!! A box with a square base and no top must have a volume of 10000cm^3. Determine the dimensions of the box that minimize the amount of materials used. The smallest dimension possible is 5cm What is the restriction in here? I already found the answer h = 13.6 and w=l = 27.1 but dont know what is the restrictions
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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saifoo.khan
  • saifoo.khan
@mathteacher1729
anonymous
  • anonymous
restriction is \(w^2h=3000\)
anonymous
  • anonymous
where is that 3000 from?? first I thought is 100 because 100x1000 gives 10000 (so cant have any volume) but when i plug it into the surface area equation, it gives a huge number..

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mathteacher1729
  • mathteacher1729
These notes might help: http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx http://tutorial.math.lamar.edu/Classes/CalcI/MoreOptimization.aspx and http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html
anonymous
  • anonymous
oh because i wasn't paying attention doh should have been \(w^2h=1000\)
anonymous
  • anonymous
can u tell me how to get it...kinda confuse
anonymous
  • anonymous
you are given that the volume is fixed, that is it must be 1000 square whatever and the base is a square with area \(w^2\) assuming you are using "w" as the variable representing the lenght of the base, and the height is "h" if you use that variable for height volume is therefore \(w^2h\) area of the base times the height.
mathteacher1729
  • mathteacher1729
The very first problem on this page is almost identical to your original problem. :) http://www.cliffsnotes.com/study_guide/Maximum-Minimum-Problems.topicArticleId-39909,articleId-39895.html
anonymous
  • anonymous
The equation I have is S = x^2 + 40000/x (when i combine the 2 equations together) so if i plug in x = 1000 , then i get 1000040 for surface area so doesnt seem restricted?
anonymous
  • anonymous
oh really, i will take a look at it! thks mathteacher
anonymous
  • anonymous
so you have two representations for the volume, one in terms of variables \(w^2h\) and the other a number you know, namely 10000, giving \[w^2h=1000\]
anonymous
  • anonymous
isnt it w^2h = 10000
anonymous
  • anonymous
@mathteacher1729 but that question only shows the min value, but not the restrictions
anonymous
  • anonymous
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anonymous
  • anonymous
restriction is first line \[x^2h=100\]
anonymous
  • anonymous
or rather \[x^2h=1000\]

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