Consider the following problem.

Maximize Z  4x1  2x2  3x3  5x4, subject to 2x1  3x2  4x3  2x4  300 8x1  x2  x3  5x4  300 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.

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(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.

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(d) Work through phase 1 step by step.

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

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(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?

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