I. Answer the following questions. (20 pts.) 1. When will you have a degenerate

Question

I. Answer the following questions. (20 pts.) 1. When will you have a degenerate solution? 2. If the problem is optimal but not feasible, how will you recover feasibility? 3. If the variables of the primal problem are all negative, the constraints of the dual are 4. By complementary slackness, the primal variables corresponding to the nonbinding dual constraints are 5. How much will the increase in the objective value be for a shadow price of 0? 6. If there will be a change in one of the objective coef- ficients, when will you apply the simplex method? . When will you use the graphical solution to solve the dual given a primal problem? 8. If there is an aditional constraint, when is this con- straint redundant? 9. In the dual simplex method, how will you choose the departing variable? 10. If there is an additional decision variable, what should be provided in the problem to determine if the opti- mal solution remains the same?

Explanation / Answer

1. If one of the basic variables take the value zero, we have a degenerate solution

2. If the primal problem is optimal but not feasible, it has an unbounded solution and hence we find the solution of the dual problem which has no feasible solution and hence feasibility cannot be recovered

3. The constraints will be of equality signs

4. By complementary slackness, the primal variables corresponding to the non binding dual constraints are positive

5. By 1e+30 by sensitivity analysis

6. When slack or surplus variables are introduced

7. If there are more number of constraints than the number of variables

8. If it's addition will not change the solution

9. The departing variable is the basic variable corresponding to the most negative value of XB in the table

10.An additional constraint should be provided

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