Work through the simplex method step by step to find all the optimal BF solutions.

1. Consider the following problem. Maximize Z _ x1 _ x2 _ x3 _ x4, subject to
x1 _ x2 _ 3

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x3 _ x4 _ 2
and
xj _ 0, for j _ 1, 2, 3, 4.
Work through the simplex method step by step to find all the optimal BF solutions.
2.* Consider the following problem. Maximize Z _ 2×1 _ 3×2, subject to
x1 _ 2×2 _ 4
x1 _ x2 _ 3
and
x1 _ 0, x2 _ 0.
(a) Solve this problem graphically.
(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) Continue from part (b) to work through the simplex method step by step to solve the problem.