Find Dimensions of the most economical can

ririwillbright

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Nov 6, 2017
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Modern frozen juice packaging often uses paper for the sides and metal for the top and bottom of the container. Suppose the paper costs only 1/3 as much as the metal and that the can contains 270 cubic centimetres of frozen juice concentrate. Find the dimensions (radius and height) of the most economical can. Give your answer to 2 decimal places.

V= nr^2h, surface area, A= 2nr^2 + 2nrh


I really need to know the answer and steps on how to obtain the answer to this question. I have tried and nothing makes sense. I am pretty clueless and I know for a fact a question like this but with different numbers will be on my exam. Please help me solve this. Thanks!
 
You say you "have tried and nothing makes sense," so that means you ought to have loads of work to share with us. Please share with us any and all work you've done on this problem, even the parts you know for sure are wrong. I'm willing to bet there's something in what you've tried that we can work with, and you're a lot closer than you think. No sense in starting back at square one if you're part way to the solution already.
 
Hey, Did you find the answer to problem. Can you please post the solution to the problem here as soon as possible, cause the assignment's due tomorrow :) thanks!!
 
… the assignment's due tomorrow :) thanks!!
Did you determine the cost function?

If so, please show us the cost function, and tell us how far you got on its derivative.

If you're still working on the cost function, where did you get stuck?

Hints: solve the volume equation for h, and substitute the result for h in the area function. Pick prices for the materials; one has to be three times larger than the other, yes? $3 and $1 would work.

After we see your efforts, we can guide you. :cool:
 
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