# What are some examples of personal or professional decisions where constrained optimization might be applied?

What are some examples of personal or professional decisions where constrained optimization might be applied? You don't have to formulate the mathematical problem, just discuss what the decision variables would be, how would you measure success (i.e., what would you maximize or minimize), and what conditions might the decision variables need to satisfy for the decisions to be considered feasible.

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Abstract

In mathematics, linear programming problems are optimization problems in which the objective function and the constraints are all linear. The model was developed during the second world war by a number of researchers. Linear programming is heavily used in many different fields, either to maximize the income or minimize the costs of a production scheme.

Standard form

Standard form is the usual and most intuitive form of describing a linear programming problem. It consists of the following three parts:

- A linear function to be maximized

maximize

- Problem constraints of the following form

- Non-negative variables

The problem is usually expressed in matrix form, and then becomes:

maximize

subject to

Other forms, such as minimization problems, problems with constraints on alternative forms, as well as problems involving negative variables can always be ...

#### Solution Summary

The solution provides detailed explanation of the origin of linear programming and the idea behind it with two examples in 656 words.