# Chapter 4 Linear Programming

In this module, we’ll learn how to solve problems where a quantity is being maximized or minimized. Additionally, this quantity is maximized or minimized in the presence of limitations.

As an example of this type of problem, let’s think about a craft brewery. Like most businesses, the brewery wants to produce different amounts of each beer so that its overall profit is as large as possible. You might think that they would produce as much as they can possible make and distribute. However, they are limited by the amount of ingredients they can buy and store as well as the amount of beer they can brew and ship. These limitations are called constraints. They prevent the brewery from ramping up production of each beer they produce. The solution to a problem like this, called a linear programming problem, is the production level of the different beers that maximizes the overall profit and meets all of the constraints.

Learning how to solves these types of problems will help you to master the objective for this chapter.

• Solve linear programming problems by graphical and algebraic techniques.

Section 1 – Solving Systems of Linear Inequalities

Section 2 – Graphical Linear Programming

Section 3 – The Simplex Method and the Standard Maximization Problem

Section 4 – The Simplex Method and the Standard Minimization Problem

Section 5 – Sensitivity Analysis

Chapter 4 Practice Solutions – 10/8/19