Question: Consider the following problem. Maximize Z = 4x1 + 2x2 + 3x3 + 5x4, Subject to and xj 0, for j = 1, 2,

Consider the following problem.
Maximize Z = 4x1 + 2x2 + 3x3 + 5x4,
Subject to

and
xj ‰¥ 0, for j = 1, 2, 3, 4.

(a) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable.

(b) Work through the simplex method step by step to solve the problem.

(c) Using the two-phase method, construct the complete first simplex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable.

(d) Work through phase 1 step by step.

(e) Construct the complete first simplex tableau for phase 2.

(f) Work through phase 2 step by step to solve the problem.

(g) Compare the sequence of BF solutions obtained in part (b) with that in parts (d) and ( f ). Which of these solutions are feasible only for the artificial problem obtained by introducing artificial variables and which are actually feasible for the real problem?

(h) Use a software package based on the simplex method to solve the problem.

2 32 4x3 2x 300 81 x3 5x300

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