# Simplex Method

**Topics:**Optimization, Linear programming, George Dantzig

**Pages:**4 (1287 words)

**Published:**March 7, 2011

Mike Smith, Todd Jones

Math212/Introduction to Finite Mathematics

February 1, 2011

The Simplex Method: 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 weeks. Sam’s offers five main product lines: basic bows, elaborate bows, bug clips, flower clips, and headbands. Sam’s want to calculate the mix of products they should bring to the fair to maximize their potential profit. Sam’s believes it is important to give their customers a variety of products. They want every product to make up at least 10% of the total items offered for sale but no more than 30%. Sam’s also knows from past festivals, that headbands are their biggest seller and want at least 15% of their product mix to be headbands. To fill their booth, they want to take at least 400 items. The cost, selling price, and labor requirements for each product are listed in Table 1. Table 1

| Cost to Make| Selling Price| Labor Required (in minutes)| Basic Bow| 0.27| 2.50| 7|

Elaborate Bow| 1.07| 4.00| 15|

Bug Clip| 0.22| 2.50| 10|

Flower Clip| 0.94| 3.00| 5|

Headband| 0.82| 4.00| 20|

This problem, as outlined above, is an example of a linear programming problem. Linear programming is part of the Optimization Techniques field of Mathematics, used for resource allocation and organization. With linear programming problems, one takes the inequalities that exist within a given situation and deduces a best case scenario under those particular conditions (Stapel, 2009). One particularly effective method of solving linear programming problems is the Simplex Method. The Simplex Method was invented in 1947 by the Mathematician George B. Dantzig. One of the greatest achievements in...

References: Carreira-Perpiñán, Miguel Á. (2010)."Simplex Method." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. Retrieved from: http://mathworld.wolfram.com/SimplexMethod.html

Stapel, Elizabeth. (2009). "Linear Programming: Introduction." Purplemath. Retrieved from:

http://www.purplemath.com/modules/linprog.htm.

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