Operation Research I (Cases of Feasible Region base on authors own Conclusion)

Operation Research I (Cases of Feasible Region base on authors own Conclusion).

1. Unbounded Feasible region with minimum optimal solution but no maximum.
2. Unbounded Feasible region with maximum optimal soulution but no minimum solution.

Operation Research I (When will an LP have an unbounded FR?)

Question: When will an LP have an unbounded FR?

Ans: If the feasible set is unbounded, there may or may not be an optimum,
depending on the specifics of the objective function. For example,
if the feasible region is defined by the constraint set {x ≥ 0, y ≥ 0},
then the problem of maximizing x + y has no optimum since any candidate
solution can be improved upon by increasing x or y; yet if the problem
is to minimize x + y, then there is an
optimum (specifically at (x, y) = (0, 0)).
Since it is unbounded, you can continue to find larger and larger solutions.
The fact that the solution space is not restricted means there are endless
possible solutions, many with extremely high values. This means there is no
set optimal solution. There are infinite possibilities which can lead to an
infinite solution.

Operation Research I (What is redundant constraint?)

Question:   What is redundant constraint?

Ans: Redundant constraints are a constraints that don't
    contribute on feasible optimal solution region.
Omitting redundant constraints will not affect
the feasible region.

Operation Research I (When is an LP infeasible?)

Question:         When is an LP infeasible?

Ans:    A linear program is infeasible if there exists
no solution that satisfies all of the constraints
    -- in other words, if no feasible solution can be
    constructed. Since any real operation that you are
    modelling must remain within the constraints of reality,
    infeasibility most often indicates an error of some kind.
   

Operation Research I (When will an LP (Linear Programming) have multiple Solution?)

Question :When will an LP (Linear Programming) have multiple Solution?


Ans: When the feasible region is unbounded.

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