Help Min & max applied problems

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In summary, to construct an open box with maximum volume using 3 square feet of material, you need to take the derivative of volume and write an equation relating length, width, or height to surface area.
  • #1

Homework Statement


An open box with a square base is to be constructed from 3 square feet of material. What dimensions will produce a box with maximun volume?


Homework Equations



v = l * w * h

The Attempt at a Solution



any other formulas involved.. ?

help... and thanx!
 
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  • #2
Since you want to maximize volume you're going to want to take the derivative of V. In order to do that you first need to get it in terms of a single variable. To do this you need a second equation relating either length width or height to some number. In your case you would want to write the equation giving the surface area of the box and go from there. Hope this helps
 

1. What are Min & Max applied problems?

Min & Max applied problems are mathematical problems that involve finding the minimum or maximum value of a certain variable given a specific set of conditions or constraints.

2. What fields of science typically use Min & Max applied problems?

Min & Max applied problems are commonly used in fields such as economics, engineering, physics, and computer science to optimize solutions and make decisions based on limited resources.

3. How do you approach solving Min & Max applied problems?

The first step in solving Min & Max applied problems is to clearly define the objective and the constraints involved. Then, mathematical techniques such as differentiation, optimization algorithms, and linear programming can be used to find the optimal solution.

4. Can Min & Max applied problems have multiple solutions?

Yes, Min & Max applied problems can have multiple solutions. Depending on the constraints and the objective, there may be multiple values that satisfy the given conditions, and it is important to evaluate all potential solutions to determine the optimal one.

5. How do Min & Max applied problems impact real-world situations?

Min & Max applied problems have a significant impact on real-world situations as they can help in making informed decisions and optimizing resources. They can be used to determine the most efficient way of allocating resources, maximizing profits, and minimizing costs in various industries and fields.

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