Question

In: Statistics and Probability

Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate...

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

80

x

+

z

60

x

+

y

w

50

y

+

z

w

50

x ≥ 0, y ≥ 0, z ≥ 0, w ≥ 0.

c = ?

(x, y, z, w) = ?

Solutions

Expert Solution

Tableau #1
x      y      z      w      s1     s2     s3     s4     -p          
1      1      0      0      -1     0      0      0      0      40   
1      0      1      0      0      -1     0      0      0      60   
1      1      0      -1     0      0      1      0      0      50   
0      1      1      -1     0      0      0      1      0      50   
1      1      1      1      0      0      0      0      1      0    

Tableau #2
x      y      z      w      s1     s2     s3     s4     -p          
1      1      0      0      -1     0      0      0      0      40   
0      -1     1      0      1      -1     0      0      0      20   
0      0      0      -1     1      0      1      0      0      10   
0      1      1      -1     0      0      0      1      0      50   
0      0      1      1      1      0      0      0      1      -40  

Tableau #3
x      y      z      w      s1     s2     s3     s4     -p          
1      1      0      0      -1     0      0      0      0      40   
0      -1     1      0      1      -1     0      0      0      20   
0      0      0      -1     1      0      1      0      0      10   
0      2      0      -1     -1     1      0      1      0      30   
0      1      0      1      0      1      0      0      1      -60  

objective function is unbounded


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