Graphical and Simplex Methods of Linear Programming
The graphical method is the more popular method to use because they are easy to use and understand. Working with only a few variables at a time they allow operations managers to compare projected demand to existing capacity. The graphical method is a trial and error approach that can be easily done by a manager or even a clerical staff. Since it is trial and error though, it does not necessarily generate the optimal plan. One downside of this method though is that it can only be used with two variables at the maximum. The graphical method is broken down into the following five steps: 1) Determine the demand in each period.

2) Determine the capacity for regular time, over time, and subcontracting each period. 3) Find labor costs, hiring and labor costs, and inventory holding costs. 4) Consider company policy that may apply to the workers or to stock levels 5) Develop alternative plans and examine their total costs. When a company has a LP problem with more than two variables it turns to the simplex method. This method can handle any number of variables as well as for certain give the optimal solution. In the simplex method we examine corner points in a methodical fashion until we arrive at the best solution which is either the highest profit or lowest cost. LP is used in a wide variety of companies in numerous applications. Airline companies use it to schedule their flights to maximize profit. Another use is for firms to figure out how much of a certain product to manufacture in order to maximize total profits. It also is used by hospitals in order to figure out the most economic diet for patients. It is also a useful tool to figure out labor scheduling for a specific time period. Other applications include product mix planning, distribution networks, truck routing, financial portfolios, and corporate restructuring. All LP problems have four properties in common. The first, LP problems seek to...

..."Operational Research" Mar. 2007, IST
LinearProgramming, an introduction
MIGUEL A. S. CASQUILHO IST, Universidade Técnica de Lisboa, Ave. Rovisco Pais, IST; 1049-001 Lisboa, Portugal
LinearProgramming is presented at an introductory level, mainly from the book by Hillier and Lieberman [2005], abridged and adapted to suit the objectives of the “Operational Research” course. It begins with segments of its third chapter.
Key...

...(Balakrishnan/Render/Stair)
Chapter 2 LinearProgramming Models: Graphical and Computer Methods
2.1 Chapter Questions
1) Consider the following linearprogramming model:
Max X12 + X2 + 3X3
Subject to:
X1 + X2 ≤ 3
X1 + X2 ≤ 1
X1, X2 ≥ 0
This problem violates which of the following assumptions?
A) certainty
B) proportionality
C) divisibility
D) linearity
E) integrality
Answer: D
Page Ref: 22
Topic:...

...TOPIC – LINEARPROGRAMMINGLinearProgramming is a mathematical procedure for determining optimal allocation of scarce resources.
Requirements of LinearProgramming
• all problems seek to maximize or minimize some quantity
• The presence of restrictions or constraints
• There must be alternative courses of action
• The objective and constraints in...

... LINEARPROGRAMMING
DATE;
5 JUNE, 14
UNIVERSITY OF CENTRAL PUNJAB
INTRODUCTION TO LINEARPROGRAMMINGLinearprogramming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are...

...unboundedness and degeneracy. 5. Use the simplex tables to conduct sensitivity analysis. 6. Construct the dual problem from the primal problem.
LinearProgramming: The SimplexMethod
LEARNING OBJECTIVES
After completing this chapter, students will be able to: 1. Convert LP constraints to equalities with slack, surplus, and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3....

...LinearProgramming History of linearprogramming goes back as far as 1940s. Main motivation for the need of linearprogramming goes back to the war time when they needed ways to solve many complex planning problems. The simplexmethod which is used to solve linearprogramming was developed by George B. Dantzig, in 1947. Dantzig, was one in who did a lot...

...The SimplexMethod: Learning Team A
Mike Smith, Todd Jones
Math212/Introduction to Finite Mathematics
February 1, 2011
The SimplexMethod: Learning Team A
Sam’s Hairbows and Accessories is a small company preparing for the next scheduled craft fair. The owners, Sam and Todd, both have full-time jobs in addition to owning the company so they are only able to spend a combined total of 80 hours labor to prepare for the fair in four...

...LinearProgramming Concept Paper
There are two types of linearprogramming:
1. LinearProgramming- involves no more than 2 variables, linearprogramming problems can be structured to minimize costs as well as maximize profits. Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult....

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