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Linear Programming Introduction

Textbook Reading: Supplemental Chapter C. This chapter is available on the publisher's website - see back cover of OM textbook for URL, or there is a pdf copy on our course Moodle page

Introduction to Linear Programming with the Graphical Method

Linear Programming

Linear Programming is making management decisions based on the limitations of your organization. In linear programming limitations are called constraints. We answer the question; How many products should we produce to maximize profit or to minimize cost.

Linear is a straight line. So we will be creating straight lines for our constraints. Programming is an old school term that predates computers and has the meaning of performing a mathematical calculation. So we are using mathematical equations to create straight lines.

The easiest way to think of constraints is to think of yourself. Do you have unlimited time and money? If you do, congratulations. If you are like most of us you have constraints that limit the maximization of your fun and excitment. The same holds true for organizations. No company has unlimited budgets, trained employees, availability of resources, and machinery.

Graphical Method

The Graphical Method is a teaching method for introducing linear programming. We graph out our constraints to help determine how many of our products (good or service) we should produce to either maximize profit or minimize cost.

Since there are only two axises on a graph and each axis represents a product, we are limited to two products and that is why the Graphical Method is just for learning the concepts. Most organizations have more than two products. Think of all the products produced by Under Armor. Since they have more than two it is impossible to graph. The graphical method does provide a thorough understanding of the topic so we may advance into Simplex Method and Excel Solver for more real world solutions.

The Plan

We will spend a few lessons on the graphical method. We will start out just setting up the problem and move forward towards a solution. For beginning steps concentrate on the set-up and understanding what the the graph represents. We will get to the solution soon enough!

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Short Power Point "How to set up problem"
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Linear Programming Graph
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Linear Programming Extreme Point
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s
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Linear Programming Simultaneous Substitution
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Linear Programming Multiplication / Mathematical Method
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Linear Programming Interpreting Results
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Linear Programming Interpretation of Results
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