Pretty simple optimization problem

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Homework Help Overview

The problem involves optimizing the cost of a closed box with a square base that must contain a specific volume of 252 cubic feet. The costs associated with the materials for the box's bottom, top, and sides vary, and the goal is to determine the dimensions that minimize the total cost.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to establish the necessary equations related to volume and cost but expresses uncertainty about deriving the next equation. Participants inquire about the areas of different sections of the box and suggest calculating these areas to facilitate cost calculations.

Discussion Status

Participants are exploring the relationships between the box's dimensions and the associated costs. Some guidance has been offered regarding the calculation of areas as a step towards determining costs, but there is no explicit consensus on the next steps or methods to be used.

Contextual Notes

The problem does not specify the areas of the different sections, which has led to some ambiguity in the discussion. The original poster is working within the constraints of the problem as presented in the text.

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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
 
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What are the areas of the different sections?
 
phsopher said:
What are the areas of the different sections?

It doesn't say, that's directly quoted from the text.
i want to say its something like
3(lw)=sides 5(lw)-bottom 2(lw)-top
 
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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