Pretty simple optimization problem

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In summary, the task is to determine the dimensions of a closed box with a square base that will minimize the cost of materials. The volume of the box is 252ft^3 and the materials used for the bottom, sides, and top cost 5$ per ft.^2, 3$ft^2, and 2$ft^2 respectively. The next step is to find another formula, possibly using the volume equation v=lwh, to derive and solve for the dimensions. The hint given is to calculate the areas of the different sections, keeping in mind that there are only two free parameters since the bottom is a square.
  • #1
wapakalypse
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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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  • #2
What are the areas of the different sections?
 
  • #3
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
 
  • #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.
 

1. What is an optimization problem?

An optimization problem is a mathematical problem that involves finding the best possible solution from a set of feasible options. This solution is typically the one that maximizes or minimizes a certain objective function.

2. How do you solve an optimization problem?

The most common method for solving optimization problems is using mathematical techniques such as calculus, linear algebra, and algorithms. These methods involve finding the optimal values of the decision variables that satisfy the given constraints and optimize the objective function.

3. What is the objective function in an optimization problem?

The objective function is a mathematical expression that defines the goal of the optimization problem. It represents the quantity that needs to be maximized or minimized in order to find the optimal solution.

4. What are the constraints in an optimization problem?

Constraints are conditions that must be satisfied in order to find a feasible solution to the optimization problem. These conditions can be mathematical equations or inequalities that limit the values of the decision variables.

5. What are some real-world applications of optimization problems?

Optimization problems have a wide range of applications in various fields such as engineering, economics, finance, and computer science. Some common examples include optimizing production processes, portfolio management, resource allocation, and route planning.

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