Question $12$

Consider the following linear program $($LP Version $2)$:

Max $Z=2^{**}x+4^{**}y$

subject $to$

$2^{**}x+3^{**}y12$

$2^{**}x+y8$

$-2^{**}x+3^{**}y6$

$x,$

Which of the following are true with respect to this linear program?

The optimal solution occurs at $(x,y)=(1\mathrm{.}5,3\mathrm{.}0).$

Exactly two answers are correct.

There are four feasible corner points in this problem.

At least one of the above constraints is redundant, that is$,$ it is not needed to define this problem's set of feasible solutions.

The values of $x$ and $y$ at the optimal solution must be whole number, that is$,$ non$-$fractional, values,