Setup

Consider the following linear program.

minimiz$\frac{e}{\frac{?}{?}}$$ x$\_1+$ x$\_22$$$2$

subject to $|$$$s{x}_1+|$ tx$\_2>=1|$$$|$

$|$$$x_1|0|$$$|$

$|$$$x_2|$$ is unconstrained

Part A

Find conditions on $|$$$s|$$ and $|$$$t|$$ to make this infeasible.

Part B

Find conditions on $|$$$s|$$ and $|$$$t|$$ to make this feasible.

Part C

Find conditions on $|$$$s|$$ and $|$$$t|$$ to make this have a unique optimal solution.

Part D

Find conditions on $|$$$s|$$ and $|$$$t|$$ to make this have multiple optimal solution.

Part E

Find conditions on $|$$$s|$$ and $|$$$t|$$ to make this unbounded.