Question: Big-M method : Find a BFS (Basic Feasible Solution). Start solution from tableau in the bottom of picture. Finding an Initial Basic Feasible Solution .

Big-M method : Find a BFS (Basic Feasible Solution). Start solution from tableau in the bottom of picture.

Big-M method : Find a BFS (Basic Feasible

Finding an Initial Basic Feasible Solution . Big-M method Basic idea Artificial variables with big M in the objective function and employ the simplex algorithm (combine Phases I and II into a single problem) Maximize z'=-3x1 - x2 - 4xz - MX6-M X7 s.t. x1 + x2 + x3 x4 + x6 =12 4x1 - x2 + x3 x3 + xy = 6 x1,x2,X3,X4,X5,X6,X720 x6 = 12 x1 - x2 x3 + x4 z'=-3x1 - x2 - 4xz - MX6-M X7 =-18M +(5M 3)x1 - x2 +(2M - 4)xz - Mx4 - Mxs 1 Z X7 = 6-4x1 + x2 - x3 + x5 X1 X2 3 -5M+3 1 -2M+4 1 1 X4 M Xg M X6 0 z 1 Xy 0 0 RHS -18M 12 X6 0 oo -1 0 1 0 X7 4 -1 1 -1 1 6

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