Reformulate this problem so that all variables have nonnegativity constraints.

1. Consider the following problem. Maximize Z__x1 _ 2×2 _ x3, subject to
3×2 _ x3 _ 120

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x1 _ x2 _ 4×3 _ 80
_3x1 _ x2 _ 2×3 _ 100
(no nonnegativity constraints).
(a) Reformulate this problem so that all variables have nonnegativity constraints.
(b) Work through the simplex method step by step to solve the problem.
(c) Use a computer package based on the simplex method to solve the problem.