Step-by-step explanation:

The Vertex Theorem for Feasible Regions

Introduction

In this lesson you will learn about the vertex theorem for feasible regions and how to apply this theorem to real-world problems. You will learn to write a system of linear inequalities to model the real-world problem. This system will then be graphed to determine the solution set for the system of inequalities. Using the vertex theorem, you will then answer the real-world problem.

Objectives

The lesson objectives for the Vertex Theorem for Feasible Regions are:

Understanding the vertex theorem.

Writing a system of inequalities for a real-world problem.

Solving the system of inequalities by graphing

Determining the vertices algebraically by solving the linear inequalities.

Using the vertex theorem to determine the answer to the real-world problem.

Introduction

A system of linear inequalities is often used to determine the best solution to a problem. This solution could be as simple as determining how many of a product should be produced to maximize a profit or as complicated as determining the correct combination of drugs to give a patient. Regardless of the problem, there is a theorem in mathematics that is used, with a system of linear inequalities, to determine the best solution to the problem.