# Simplex Method

**Topics:**Linear programming, Optimization, Simplex algorithm

**Pages:**4 (1192 words)

**Published:**March 13, 2011

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...

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