# Follow the instructions for the following problem. Minimize Z _ 3×1 _ 2×2 _ 7×3, subject to

1. Follow the instructions for the following problem. Minimize Z _ 3×1 _ 2×2 _ 7×3, subject to

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_x1 _ x2 _ x3 _ 10
2×1 _ x2 _ x3 _ 10
and
x1 _ 0, x2 _ 0, x3 _ 0.
2. Follow the instructions for the following problem. Minimize Z _ 3×1 _ 2×2 _ x3,
to
x1 _ x2 _ x3 _ 7
3×1 _ x2 _ x3 _ 10
and
x1 _ 0, x2 _ 0, x3 _ 0. Lbel each of the following statements as true or false, and then justfy your anwer.
(a) Whn a linear programming model has an equality constraint, an artificial variable is introduced into this constraint in order to start the simplex method with an obvious initial basic solution
that is feasible for the original model.
(b) When an artificial problem is created by introducing artificial variables and using the Big M method, if all artificial variables in an optimal solution for the artificial problem are equal to zero, then the real problem has no feasible solutions.
(c) The two-phase method is commonly used in practice because it usually requires fewer iterations to reach an optimal solution than the Big M method does.

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