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.