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# Slides_17 - Lecture 17 The Simplex Method(Winston Chapter 4...

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1 Lecture 17 The Simplex Method (Winston, Chapter 4) The general idea x 1 (2 units) x 2 (2 units) P 1 P 5 P 4 P 3 P 2 Observation 1: If an LP has an optimal solution, then there is also a vertex of the simplex that is optimal (here P 4 ). General idea: STEP 1: Start with a vertex. STEP 2: If that vertex is not optimal, then go to an adjacent vertex that improves the objective function value. And go back to Step 2.

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The general idea x 1 (2 units) x 2 (2 units) P 1 P 5 P 4 P 3 P 2 For example, we might generate P1 P2 P3 P4 (stop.) Questions: 1. How do we find a starting vertex? 2. How do we find an “improving” vertex? 3. How do we determine if current solution is optimal? Example We will discuss the simplex method by looking at an example. Let’s solve the following LP (Example II) by the simplex method. s.t. 6x 1 + 5x 2 60 x 1 + 2x 2 15 x 1 8 x 1 , x 2 0. max
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Slides_17 - Lecture 17 The Simplex Method(Winston Chapter 4...

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