# 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.

1. Consider the following problem. Maximize Z__2x1 _ x2 _ 4×3 _ 3×4, subject to
x1 _ x2 _ 3×3 _ 2×4 _ _4

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x1 _ x2 _ x3 _ x4__1
2×1 _ x2 _ x3 _ x4 _ _2
x1 _ 2×2 _ x3 _ 2×4 _ _2
and
x2 _ 0, x3 _ 0, x4 _ 0
(no nonnegativity constraint for x1).
(a) Reformulate this problem to fit our standard form for a linear programming model presented in Sec. 3.2.
(b) 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.
(c) Using the two-phase method, construct row 0 of the first simplex tableau for phase 1.
(d) Use a computer package based on the simplex method to solve the problem.

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