Consider the following optimization problem:

MIN:

X$+$X

Notifications$-$

Guide Me

Subject to:

$-4$X$1+4$X$21$

$-8$X$110$X$215$

X$1,$ X$20$

a$.$ What is the optimal solution to the problem? Round your answers to two decimal places, if necessary.

X$1$

X$2$

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

X$1$

X$2$

c$.$ What general principle of integer programming is illustrated by this question?