Max z 2 x 1 3 x 2 4 x 3 3 x 1 4 x 2 x 3 12 (1) 4 x 1 3 x 2 2 x 3 24 (2) x 1 , x 2 , x 3 0 For the above linear programming (LP) formulation, use matrix notation approach of the Simplex Method to answer questions a and b Let s 1 and s 2 be the variables used to convert constraints (1) and (2) to standard form respectively a Take the initial basis where x 2 and s 2 are the basic variables Find the values of all variables (basic and nonbasic) and the objective function value at this basis using the formulas of the Simplex Method b Check whether this current solution is optimal If not, determine i which variable will enter the basis ii which variable will leave the basis iii the value of the entering variable in the new basis

Question

Max z   2 x 1   3 x 2   4 x 3  3 x 1   4 x 2   x 3 12 (1) 4 x 1   3 x 2   2 x 3 24 (2) x 1 , x 2 , x 3 0 For the above linear programming (LP) formulation, use matrix notation approach of the Simplex Method to answer questions a and b  Let s 1 and s 2 be the variables used to convert constraints (1) and (2) to standard form respectively  a  Take the initial basis where x 2 and s 2 are the basic variables  Find the values of all variables (basic and nonbasic) and the objective function value at this basis using the formulas of the Simplex Method  b  Check whether this current solution is optimal  If not, determine i  which variable will enter the basis ii  which variable will leave the basis iii  the value of the entering variable in the new basis

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Question: Max z = 2 x 1 + 3 x 2 - 4 x 3 -3 x 1 + 4 x 2 + x 3 12

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