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Lecture25aa_1

# Lecture25aa_1 - Lecture Simplex Method for Maximization...

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Lecture 3/26/08 Simplex Method for Maximization Problems 1. Use of tableaus

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Terminology Review Given an LP with n variables (including slack, surplus) and m constraints. 1.Basic solution a. Set n-m of the variables to zero (1). Nonbasic variables (NBV) b. Solve for values of the remaining m variables. (1) Basic variables (BV) (2) Basis = set of BV in a basic solution 2. A basic solution that is feasible is a bfs.
6 Steps of the Simplex Algorithm 1. Convert LP to standard form 2. Obtain bfs (if possible) from standard form 3. Determine if current b.f.s is optimal 4. If not optimal a. Determine which NBV should be a BV b. Determine which BV should be a NBV. 5. Use elementary row operations (ero’s) to find a better bfs. 6. Go back to step 3

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Application of 6 Steps to Example Given LP Max z=2x 1 + 2.5x 2 such that x 1 + 2x 2 350 2 x 1 + x 2 400 x i 0 for i=1,2
Application of 6 Steps to Example 1. Convert LP problem to standard form Row 0 z - 2x 1 - 2.5x 2 =0 Row 1 x 1 + 2x 2 + s 1 = 350 Row 2 2 x 1 + x 2 + s 2 = 400 x i ,s i 0 for i=1,2 2. Obtain a bfs from the standard form Set x 1 = x 2 = 0 , Then s 1 = 350, s 2 = 400, z=0 BV z=0 s 1 =350 s 2 =400

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Lecture25aa_1 - Lecture Simplex Method for Maximization...

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