Simplex Method Paper
Many people may be wondering exactly what the simplex method is. The simplex method definition is a method for solving linear programming problems. According to Barnett, Byleen, and Karl (2011) the simplex method is used routinely on applied problems involving thousands of variables and problem constraints. George B. Dantzig developed the simplex method in 1947. In this paper the topic of discussion includes how to solve a simplex method problem that a private artist creates paintings in a variety of sizes. Below describes the problems that the artist is facing.

Painting A: 8 X 10: requires 20 hours of labor, 1 hour to mat and frame Painting B: 10 X 24: requires 60 hours of labor, 1 hour to mat and frame
Painting C: 24 X 48: requires 80 hours of labor, 2 hours to mat and frame The artist is only able to spend 20 hours per week creating paintings. The profits for each painting are: A: $400, B: $800, C: $1000

How many paintings should the artist create (and what sizes) within 1 year to maximize profits?
What would the artist’s maximum profits be?
Objective Function and Constraints
To find the objective function and constraints present in the situation described evaluation of the elements present is needed. The objective function is the equation to determine the profit from selling paintings in the three sizes available. For the purpose of this scenario the variables A, B, and C are used, when sold each make a profit of $400, $800, and $1000 respectively. When displayed as an equation, the objective function is

P = 400(A) + (800)B + (1000(C)
Constraints that exist in this system can easily be found in the question. The constraints are in the number of hours the artist has available to work on painting. In the circumstance of the case in point the artist can spend 20 hours per week devoted to painting. This amounts to 1040 hours yearly, or rather 20 hours weekly for 52 consecutive...

...The simplexmethod is used regularly on applied problem involving thousands of variables and problem constrains (Barnett, Ziegler, & Byleen, 2011). This was the method chosen when Wintel Technologies needed to figure out the best way to utilize time and schedule for their field engineers. With a busy schedule and being needed on several different areas in the United States, the simplexmethod was brought in to decide where...

...unboundedness and degeneracy. 5. Use the simplex tables to conduct sensitivity analysis. 6. Construct the dual problem from the primal problem.
Linear Programming: 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. Interpret the meaning of...

...of its third chapter.
Key words: linear programming; simplexmethod.
I. Fundamentals and scope
Based on a prototype example, Linear Programming is presented, as well as the simplexmethod of resolution. This method was first presented by G. B. Dantzig in 1947 [MacTutor, 2007]. The text is based on the book by Hillier and Lieberman [2005], and begins with segments of the third chapter of the book.
II. Explanation...

...and SimplexMethods 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...

...Algorithm to Calculate Basic Feasible Solution using SimplexMethod
Abstract:
The problem of maximization/minimization deals with choosing the ideal set of values of variables in order to find the extrema of an equation subject to constraints. The simplexmethod is one of the fundamental methods of calculating the Basic Feasible Solution (BFS) of a maximization/minimization. This algorithm implements the...

...Unit 1 Lesson 9 : The Big M Method
Learning outcomes • The Big M Method to solve a linear programming problem.
In the previous discussions of the Simplex algorithm I have seen that the method must start with a basic feasible solution. In my examples so far, I have looked at problems that, when put into standard LP form, conveniently have an all slack starting solution. An all slack solution is only a possibility when all of the...

...USING STEPPING STONE AND MODI METHODS TO SOLVE TRANSPORTATION PROBLEMS
BY
ABDUSSALAM MUHAMMAD MUSTAPHA
09/211306009
A SEMINAR PAPER PRESENTED TO THE DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, USMANU DANFODIYO UNIVERSITY, SOKOTO IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF MASTER OF SCIENCE (MATHEMATICS)
SUPERVISORY TEAM:
MAJOR SUPERVISOR: DR. U. A. ALI
CO – SUPERVISOR I: DR. I. J. UWANTA
CO – SUPERVISOR II: DR. MU’AZU...

...
Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair)
Chapter 2 Linear Programming Models: Graphical and Computer Methods
2.1 Chapter Questions
1) Consider the following linear programming 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: Developing a Linear...

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