Consider the all$-$integer linear optimization problem below:

Max$5x_1+8x_2$

Subject to $($s$.$t$)$

$6x_1+5x_{2}30$ Constraint$1$

$9x_1+4x_{2}36$ Constraint $2$

$11+2210$ Constraint $3$

$x_1,x_{2}0$ and integer

$($a$)$ What is the optimal value of the decision variable X$1?$

Enter just the numeric value

$($b$)$ What is the optimal value of the decision variable $x_2?$

Enter just the numeric value

$($c$)$ Find the optimal solution to the optimization problem.

$($d$)$ What are the values of the slack variables in constraint $1?$