Question 1

If two constraints do not intersect in the positive quadrant of the graph, then&#10;A) The problem is infeasible&#10;B) The solution is unbounded&#10;C) One of the constraints is redundant&#10;D) None of the above

Accepted Answer

If two constraints do not intersect in the positive quadrant, it means there is no common solution that satisfies both constraints simultaneously in the feasible region, leading to an infeasible problem.

Question 2

The solution space (region) of an LP problem is unbounded due to&#10;A) An incorrect formulation of the LP model&#10;B) Objective function is unbounded&#10;C) Neither a nor b&#10;D) Both a & b

Accepted Answer

An unbounded solution space in an LP problem is typically due to the constraints allowing infinite feasible solutions, not necessarily due to incorrect formulation or the objective function being unbounded.

Question 3

While solving a LP model graphically, the area bounded by the constraints is called&#10;A) Feasible region&#10;B) Infeasible region&#10;C) Unbounded solution&#10;D) None of the above

Accepted Answer

The feasible region in a graphical LP model represents all the possible points that satisfy all the constraints simultaneously, including both the objective function and any limitations or requirements set by the problem.

Question 4

While solving a LP problem, infeasibility may be removed by&#10;A) Adding another constraint&#10;B) Adding another variable&#10;C) Removing a constraint&#10;D) Removing a variable

Accepted Answer

Removing a constraint can potentially remove the infeasibility in a Linear Programming (LP) problem by relaxing the system, thus allowing for a feasible solution space.

Question 5

If a non-redundant constraint is removed from an LP problem then&#10;A) Feasible region will become larger&#10;B) Feasible region will become smaller&#10;C) Solution will become infeasible&#10;D) None of the above

Accepted Answer

Removing a non-redundant constraint from a Linear Programming (LP) problem means that one less restriction is applied to the feasible region, allowing more solutions to be considered feasible. Thus, the feasible region becomes larger.

Question 6

If one of the constraint of an equation in an LP problem has an unbounded solution, then&#10;A) Solution to such LP problem must be degenerate&#10;B) Feasible region should have a line segment&#10;C) Alternative solutions exist&#10;D) None of the above

Accepted Answer

The answer of If one of the constraint of an...

Question 7

The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that&#10;A) The solution be optimal&#10;B) The rim conditions are satisfied&#10;C) The solution not be degenerate&#10;D) All of the above

Accepted Answer

The rim conditions, which refer to the supply and demand constraints being met, must be satisfied for any initial solution of a transportation problem. This ensures that the total supply equals the total demand across all sources and destinations.

Question 8

During an iteration while moving from one solution to the next, degeneracy may occur when&#10;A) The closed path indicates a diagonal move&#10;B) Two or more occupied cells are on the closed path but neither of them represents a corner of the path.&#10;C) Two or more occupied cells on the closed path with minus sign are tied for lowest circled value&#10;D) Either of the above

Accepted Answer

Degeneracy occurs when two or more occupied cells on the closed path with a minus sign have the same lowest circled value, leading to ambiguity in selecting the next solution.

Deck 6: LP and Transportation Models: Assumptions, Limitations, and Solutions