QUICK QUESTION: Minimizing Restrictions

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SUMMARY

The problem involves determining the dimensions of a box with a square base and no top that must contain a volume of 10,000 cm³ while minimizing surface area. The equations used are volume V = x²y and surface area SA = x² + 4xy. By isolating y using the volume equation, y is expressed as y = 10,000/x². The solution yields dimensions of x = 27.1 cm and y = 13.6 cm, with the constraint that x must be greater than or equal to 5 cm.

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Homework Statement



Question: a box with a square base and no top must have a volume of 10,000cm^3. if the smallest dimensions in any direction is 5cm, the determine the dimensions of the box that minimize the amount of material used.

Homework Equations



V=x^2&y
SA=x^2+4xy
(isolate for y using given volume in V equation to obtain y=10,000/x^2)

The Attempt at a Solution



SA=x^2+4x(10,000/x^2)

when solved...x=27.1
y= 13.6I have an answer on what the dimensions are, but what do i use as my limitations besides what my x values are. I know i have to use x>or=5...for some reason i can never figure these limitations/restrictions out...
 
Last edited:
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"must have a volume of 10,000cm^3" Sounds like a restriction to me.
 

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