$(15$ points$)$ Answer the following true$/$false questions. If your answer is "false", provide a brief explnnation of a counter$-$example to support your claim.

i$.$ Infeasibility means that there are no solutions that can satify all constraints simultaneously.

ii$.$ If an LP problem has less constraints than variables, it is guaranteed to be infeasible.

iii. It's poesible for a linear program to be both infeasible and unbounded.