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WORKSHEET(6.1)

# WORKSHEET(6.1) - WORKSHEET(6.1 A Geometric Introduction to...

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WORKSHEET (6.1) A Geometric Introduction to the Simplex Method Key Terms: Standard Maximization Problem in Standard Form Slack Variables Basic and Nonbasic Variables: Basic Solutions and Basic Feasible Solutions Standard Maximization Problem in Standard Form Example: Maximize 2 1 10 15 x x P + = Objective function Subject to 10 2 2 1 + x x Problem constraints 10 3 2 1 + x x 0 , 2 1 x x Nonnegative constraints Step1 : Convert the Inequalities to Equalities. In order to turn the constraint 10 2 2 1 + x x into an equality, we add a new variable 1 s to the left side of the inequality to create the equality 10 2 1 2 1 = + + s x x . As 1 x and 2 x change, the variable 1 s continually “takes up the slack” to ensure that an equality exists. 10 2 2 1 + x x 10 3 2 1 + x x (The number of problem constraints = The number of slack variables) The system above has infinitely many solutions. Step 2 : Find Basic Solutions and Basic Feasible Solutions.

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WORKSHEET(6.1) - WORKSHEET(6.1 A Geometric Introduction to...

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