Essay about Simplex Method

1207 Words Mar 28th, 2011 5 Pages
Simplex Method Paper

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
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How many artists are we going to have working on the paintings, which sizes would maximize their profit, should they focus on one size, or a mixture to make the most money from their work? Also can they work on more than one painting at a time? Given the above figures it would make sense if there was one artist that could create only one painting at a time, to go for the 8x10s. However, if the artist can divide their time, a mixture of sizes would net the best profit. The Simplex Tableau is a way to decide which paintings and how many would accomplish this task.
The Results of the Solution Given the constraints of this problem, the only restriction placed upon the artist of working 20 hours a week we must maximize the profit. To give perspective to this problem we are extending out the labor time to a year’s worth of work. This means that at 20 hours a week, a total of 1040 labor hours are available per year. We know that the artist can paint three different sizes with the only variance in the time required to mat and frame the paining. Knowing this information we developed the equation of P=400x1+800x2+1000x3. This shows the profits maximized when assigning values to x1 , x2, and x3. The artist’s constraints are that the yearly total of labor hours cannot exceed 1040 so that leads us to our constraint inequality 21x1+61x2+82x3 ≤1040. It is obvious that a painter cannot create a negative number of paintings

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