E ach of the following table is associated with a maximization model. One or more of the following descriptions applies to each table:

(i) optimal, (ii) shows problem is unbounded, (iii) shows problem is infeasible, (iv) there are alternate optima, (v) the problem is feasible, but the current solution is not optimal.

Decide which of the above descriptions applies to each table. If there are alternate optima, identify at least two of the corner points that are optimal. Justify all your answers.

(a)

Basic z x1 x2 s1 s2 Soln.

z 1 0 0 3 0 90 x1 0 1 1/3 1/3 0 10 s2 0 0 3 -1/2 1 12

(b)
Basic z x1 x2 x3 s1 s2 s3 Soln.
z 1 -1 0 0 1 0 2 1,400 x2 0 1/2 1 0 -1/2 0 2/3 100 x3 0 0 0 1 1/2 0 -1/4 100 s2 0 0 0 0 -1/2 1 -1/3 200 (c)
Basic x1 x2 s1 s2 Soln.
z 0 1 3 0 90 x1 1 -1/3 1/3 0 10 s2 0 -3 -1/2 1 12 (d)
Basic x1 x2 s1 s2 Soln.
z -9 -6 0 0 0 s1 -1 1 1 0 11 s2 -2 3 0 1 15