Choose the best describing statement (a, b, c, d, e, or f) for each of the four tableaus below. Explain why you chose your choice, and answer your choice's corresponding question.

a) The tableau exhibits an optimal solution with a unique optimal solution. What is the solution value and the solution vector? 

b) The tableau exhibits optimal with multiple optimal solutions. Indicate the variable that enters the basis and the variable that leaves the basis to form this alternative optimal solution. 

c) The tableau exhibits a feasible solution that is not yet optimal but further iterations are possible. 

Indicate the entering variable and the leaving variable. 

d) The tableau exhibits an infeasible point to the original problem, but further iterations are possible. Indicate the entering variable and the leaving variable. 

e) The tableau indicates that the problem is infeasible (i.e., there are no feasible points to the problem. What causes this infeasibility, i.e., indicate at least one constraint that cannot be satisfied. 

f) The tableau indicates that the problem is unbounded. Indicate what variable is causing the problem to be unbounded.

TABLEAU 1

	Z	x1	x2	x3	s1	s2	s3	rhs
z	1	0	-0.5	0	0	0.5	0	10
s1	0	0	2.5	0	1	-1.5	1	10
x3	0	0	-1	1	0	1	-1	0
x1	0	1	1.5	0	0	-0.5	1	10

TABLEAU 2

	Z	x1	x2	x3	x4	s1	s2	s3	rhs
z	1	0	-2	12	1	0	-3	0	0
s1	0	0	-2	9	1	1	-9	0	0
x1	0	1	1/3	-2	-1/3	0	1	0	0
s3	0	0	2	-9	-1	0	9	1	1

TABLEAU 3

	Z	x1	x2	e1	a1	s2	s3	rhs
z	1	-1	-1	0	0	0	0	-3
a1	0	2	1	-1	1	0	0	3
s2	0	3	1	0	0	1	0	7/2
s3	0	1	1	0	0	0	1	1

TABLEAU 4

	Z	x1	x2	e1	a1	s2	s3	rhs
z	1	0	0	0	0	0	1	-1
a1	0	0	-1	-1	1	0	-2	1
s2	0	0	-2	0	0	1	-3	1/2
x1	0	1	1	0	0	0	1	1