Formula sheet (6.3)

Formula sheet (6.3) - maximization problem. Original...

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Formula sheet (6.3) Transpose of a Matrix Given a mxn matrix A, the transpose of A is the nxm matrix T A obtained by putting the first row of A into the first column of T A , the second row of A into the second column of T A . = i f c h g e d b a A = i h g f c e b d a A T Formation of theDual Problem Given a minimization problem with constraints, Step 1: Form matrix A using coefficients of the constraints and the objective function. Step 2: Interchange rows and columns of A to get T A . Step 3: Use rows of T A to write down the dual maximization problem with constraints. Fundamental Principle of Duality A minimization problem has a solution if and only if its dual problem has a solution. If a solution exists, then the optimal value of the minimization problem is the same as the optimal value of the
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Unformatted text preview: maximization problem. Original Problem Dual Problem 45 16 27 3 50 5 2 2 1 2 1 2 1 2 1 ≥ ≥ + = ≥ + ≥ + x x x x C x x x x 27 50 4 3 5 16 2 2 1 2 1 2 1 2 1 ≥ ≥ + = ≤ + ≤ + x x y y P y y y y Solution of a minimization Problem Given a minimization problem with nonnegative coefficients in the objective function, Step 1: Write all constraints as ≥ inequalities. Step 2: Form the dual problem. Step 3: Use variables from minimization problem as slack variables. Step 4: Use simplex method to solve this problem. Step 5: If solution exist, read it from bottom row. If dual problem has no solution, neither does the original problem....
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This note was uploaded on 09/08/2010 for the course MATH 70 at San Jose State.

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