How do I set up an optimization problem?

In summary, the conversation is discussing how to set up an optimization problem for a closed rectangular box with a square base and a given surface area. The goal is to maximize the volume of the box, and the suggested approach is to express the surface area and volume as functions of the given variables and use them to find the optimal dimensions.
  • #1
Raidkha
4
0
How do I set up an optimization problem??

Homework Statement


A closed reactangular box, with a square base x by x cm and height h cm. The surface area is 8cm^2. Find the maximum

* I know how to find the critical points and everything else, but I don't know how set the problem up. I have a really huge problem with sitting the problem up. PLEASE GIVE ME SOME TIPS ON HOW TO DO THAT!
 
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  • #2


Hi Raidkha
You didn't finish exposing the problem, but I suppose you want to maximize the volume of the box
What you should do is put in formulas what the problem says
so you express the surface as a function of x and h, and then the volume.
the given surface will allow you to express h as a function of x (or the other way around), which you then plug in the volume formula which you then try to maximize
 

1. What is an optimization problem?

An optimization problem is a mathematical problem that involves finding the best solution or set of solutions from a given set of alternatives. It is used to maximize or minimize a specific objective or goal, subject to a set of constraints.

2. What are the steps to set up an optimization problem?

The steps to set up an optimization problem include identifying the objective function, defining the decision variables, determining the constraints, and specifying the optimization method. It is also important to validate the model and interpret the results.

3. How do I determine the objective function in an optimization problem?

The objective function is the measure of success or the goal that you want to achieve. It could be a single variable or a combination of variables that need to be maximized or minimized. It is typically represented as a mathematical equation or formula.

4. How do constraints affect an optimization problem?

Constraints are restrictions or limitations that must be considered when solving an optimization problem. They can be in the form of mathematical equations or inequalities that limit the values that the decision variables can take. Constraints can greatly impact the feasibility and optimality of the solution.

5. What are some common optimization methods used in setting up an optimization problem?

Some common optimization methods include linear programming, quadratic programming, integer programming, and nonlinear programming. These methods use algorithms to find the optimal solution by iteratively adjusting the values of the decision variables to meet the objective function and constraints.

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