Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Minimize c = x + y + z + w subject to x + y ≥ 60 x + z ≥ 50 x + y − w ≤ 30 y + z − w ≤ 30 x ≥ 0, y ≥ 0, z ≥ 0, w ≥ 0.
Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Minimize c = x + y + z + w subject to x + y ≥ 60 x + z ≥ 50 x + y − w ≤ 30 y + z − w ≤ 30 x ≥ 0, y ≥ 0, z ≥ 0, w ≥ 0.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
Question
Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.)
Minimize
c = x + y + z + w
subject tox | + | y | ≥ | 60 | ||||
x | + | z | ≥ | 50 | ||||
x | + | y | − | w | ≤ | 30 | ||
y | + | z | − | w | ≤ | 30 |
x ≥ 0, y ≥ 0, z ≥ 0, w ≥ 0.
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