Consider the following optimization problem:

MIN: X$1+$ X$2$

Subject to: $4$X$1+4$X$2<=1$

$8$X$1+11$X$2>=14$

X$1,$ X$2>=0$

$($a$)$ What is the optimal solution to this LP problem?

$($X$1,$ X$2)=$

$($b$)$ Now suppose that X$1$ and X$2$ must be integers. What is the optimal solution?

$($X$1,$ X$2)=$