Min $22$X$+27$Y

Subject to

$2$ X$+3$ Y $>30($constraint $1)$

X $+$ Y $>8($constraint $2)$

$2$ X $+$ Y $>20($constraint $3)$

X $,$ Y $>0($non$-$negativity$)$

Which of the following statements is correct? $($there might be more than one correct statement$)$

Group of answer choices

This problem has an unbounded solution

The optimal solution is X$=15$ and Y$=0$

This problem has a unique optimal solution

This problem has a multiple optima solution

This problem is infeasible