WORKSHEET (6.3) - WORKSHEET(6.3 Part I Solve the following...

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WORKSHEET (6.3) Part I Solve the following minimization problem by maximizing the dual: Minimize 2 1 2 x x C + = Subject to 6 2 1 + x x 12 3 2 1 + x x 0 , 2 1 x x Step1 : Form a matrix A, using the coefficients and constants in the problem constraints and the objective function. = A Step 2: Interchange rows and columns of A to get T A . = A = T A Step 3: Use rows of T A to write down the dual maximization problem with constraints.
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Original Problem Dual Problem Minimize 2 1 2 x x C + = Maximize 2 1 12 6 y y P + = Subject to 6 2 1 + x x Subject to 1 2 1 + y y 12 3 2 1 + x x 2 3 2 1 + y y 0 , 2 1 x x 0 , 2 1 y y Corner Points Corner Points ( x , y ) 2 1 2 x x C + = (0,6) (3,3) (12,0) Step 4: Write the initial system of the dual problem, using the variables from minimization problem as slack variables.
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