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Pretty simple optimization problem

  • #1
A closed box with a square base is to contain 252ft^3. The bottom costs 5$ per ft.^2, the top is 2$ft^2 and the sides cost 3$ft^2. Find the dimensions that will minimize the cost.



As for equations we have v=lwh and I'm not sure as to how to find the next relative equation.



I just need to find another formula so I can derive and solve. Any help is much appreciated.
Thankss
 

Answers and Replies

  • #2
180
4
What are the areas of the different sections?
 
  • #3
What are the areas of the different sections?
It doesnt say, thats directly quoted from the text.
i wanna say its something like
3(lw)=sides 5(lw)-bottom 2(lw)-top
 
  • #4
180
4
That was meant to be a hint for your next equation. Calculate the areas and you can work out the cost from that. Note that there are only two free parameters since the bottom is a square.
 

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