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Unformatted text preview: Slide 1 Simplex Method Finite Math Section 5.1 Slide 2 Standard Maximization Problems A linear programming problem is a standard maximization problem if the following conditions are met: The objective function is linear and is to be maximized. The variables are all nonnegative (i.e., x ≥ 0, y ≥ 0, z ≥ 0, …). The structural constraints are all of the form ax + by + … ≤ c, where c ≥ 0. Slide 3 Examples The following constraints are in the form appropriate for a standard maximization problem: 2x – 3y ≤ 9 –5x + 2y ≤ 11 x + 5y + 2z ≤ 8 The following constraints are not in the form appropriate for a standard maximization problem: x + 4y ≥ 3 2x + y ≤- 4 –2x + 3z ≥ y + 11 Slide 4 Slack Variables The first step in the simplex method is to convert each structural constraint into an equality by adding a slack variable to the left side and replacing the inequality symbol with an equal sign. Slide 5 Slack Variables Each constraint requires a different slack variable. A slack variable “takes up the slack” of the inequality and ensures equality. For any point in the feasible region of a standard maximization problem, the value of each slack variable is nonnegative....
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This note was uploaded on 01/12/2012 for the course MATH 2053 taught by Professor Pamelasatterfield during the Spring '08 term at NorthWest Arkansas Community College.
- Spring '08