1. True or False.
a. If an optimal solution is degenerate, then there are alternate optimal solutions of the LP problem.
b. If the objective function coefficient in the cj row above an artificial variable is – M, then the problem is a minimization problem.
c. If the primal problem has an unbounded solution, its dual will also have an unbounded solution.
d. The feasible space of some LP problems can be non-convex.
e. Artificial variables are added to a linear programming problem to aid in the finding an optimal solution.
3. Multiple Choice:
i. If an optimal solution is degenerate, then
(a) there are alternative optimal solutions
(b) the solution is infeasible
(c) the solution is of no use to the decision-maker
(d) none of the above
ii. To formulate a problem for solution by the simplex method, we must add artificial variable to
(a) only equality constraints
(b) only ‘greater than’ constraints
(c) both (a) and (b)
(d) none of the above
iii. If any value in xB – Column of final simplex table is negative, then the solution is (a) unbounded
(b) infeasible
(c) optimal
(d) none of the above
iv. If all aij values in the incoming variable column of the simplex table are negative, then (a) solution is unbounded
(b) there are multiple solutions
(c) there exist no solution
(d) the solution is degenerate
v. If an artificial variable is present in the ‘basic variable’ column of optimal simplex table, then the solution is
(a) infeasible (b) unbounded
(c) degenerate (d) none of the above
vi. The dual of the primal maximization LP problem having m constraints and n non negative variables should
(a) have n constraints and m non-negative variables
(b) be a minimization LP problem
(c) both (a) and (b)
(d) none of the above
vii. For any primal problem and its dual,
(a) optimal value of objective functions is same
(b) primal will have an optimal solution if and only if dual does too
(c) both primal and dual cannot be infeasible
(d) all of the above
viii. When an additional variable is added in the LP model, the existing optimal solution can further be improved if
(a) cj – zj = 0 (b) cj – zj = 0
(c) both (a) and (b) (d) none of the above
ix. Addition of an additional constraint in the existing constraints will cause a (a) change in objective function coefficients (cj)
(b) change in coefficients aij
(c) both (a) and (b)
(d) one of the above
x. A constraint in an LP model is redundant if
(a) it does not affect the feasible solution region
(b) the solution is unbounded