The tableaus below were obtained by performing the simplex method for a particular LP problem in which the objective function was being maximized. However, the tableaus have been shuffled around into a "random" order, and the value of the objective function value has been deleted.

a) for each tableau, either indicate that the solution is optimal or indicate the variable leaving the basis and the variable entering the basis with clear explanations.

b) Number the tableaus to indicate an order in which the tableaus could have occurred during the execution of the simplex method.

Tableau 1:

Basic Var	z	x1	x2	x3	x4	x5	x6	RHS
z	1	0	0	-1125	0	1.125	0	-------
x1	0	1	0	1	0	0	0	1
x4	0	0	0	1.25	1	0	0	0.75
x2	0	0	1	-1.25	0	0	0	0.25
x6	0	0	0	225	0	-0.12	1	75

Tableau 2:

Basic Var	z	x1	x2	x3	x4	x5	x6	RHS
z	1	0	-4500	4500	0	0	0	------
x1	0	1	0	1	0	0	0	1
x4	0	0	1	0	1	0	0	1
x5	0	0	4000	-5000	0	1	0	100
x6	0	0	500	-400	0	0	1	200

Tableau 3:

Basic var	z	x1	x2	x3	x4	x5	x6	RHS
z	1	0	0	0	0	0.5	5	-----
x1	0	1	0	0	0	0.001	0	0.667
x4	0	0	0	0	1	0	-0.01	0.333
x2	0	0	1	0	0	0	0.006	0.667
x3	0	0	0	1	0	0	0.004	0.333

Tableau 4:

Basic Var	z	x1	x2	x3	x4	x5	x6	RHS
z	1	-4500	-4100	0	0	0	0	-----
x3	0	1	0	1	0	0	0	1
x4	0	0	1	0	1	0	0	1
x2	0	5000	4000	0	0	1	0	6000
x6	0	400	500	0	0	0	1	600