Consider the following IP problem.

Maximize $z=3x_1+2x_2,$

subject to

Constraint $1$: $2x_1+3x_{2}35,$

Constraint $2$: $3x_1+x_{2}25,$

Constraint $3$: $x_1,x_{2}0,$

Constraint $4$: $x_1,x_2=$ non$-$negative integer,

where $x_1$ and $x_2$ represent the decision variables. Solve this IP problem and answer the following questions.

a$.$ What are the values of $x_1$ and $x_2$ at the optimal solution? What is the maximum value of $z?$

$\backslash$table$[[$Value of $x_1$ at the optimal solution$],[$Value of $x_2$ at the optimal solution$],[$Maximum value of $z$