You are given the tableau below for a maximization problem. Give conditions on t

Question

You are given the tableau below for a maximization problem.

Give conditions on the unknowns a1, a2, a3, a4, a5, b, and c that make the following statements true:

a) (3 points) The current solution is optimal.

b) (3 points) The current solution is optimal, and there are alternative optimal solutions.

c) (3 points) The LP is unbounded (in this part, assume that b ? 0).

d) (3 points) The next simplex iteration corresponds to a degenerate solution.

e) (3 points) The current solution is infeasible.

(Note that for each statement, give the conditions on all unknowns. Even if the unknown can take any value, state that it can take any value. Some unknowns can take same value for all statements. For example, F can only be equal to 1 (to satisfy the canonical form in a simplex tableau), whatever the statement is. Therefore, when giving conditions, state that F=1 for each statement. Also consider each statement independently.)

Explanation / Answer

a) The current solution is optimal.

c1 >= 0; c2 >= 0; F = 1; a4 = 0; a5 = 1; a1, a2, a3, b can be any real numbers.

b) The current solution is optimal, and there are alternative optimal solutions.

c1 >= 0; c2 >= 0; F= 1; a4 = 0; a5 = 1needs for the optimal solution

Since F >0, then a3 >0; c1, a2 = 0 can be brought x1 into the basis without changing the function value.

c) The LP is unbounded (in this part, assume that b 0)

F= 1 for feasibility

Given this, the problem is unbounded at C1< 0 and a2, a3 <= 0

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