Consider the following LP problem.

Maximize

Subject to

Constraint $1$: $,2x_1+3x_{2}40,$

Constraint $2$: $,3x_1+x_{2}30,$

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

where $x_1$ and $x_2$ represent the decision variables. Solve the LP problem to 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 $z?$

Note: Round your answers to $2$ decimal places.

b$.$ Identify the binding and nonbinding constraints and report the slack value, as applicable.

Note: If the answer to constraints is "Non$-$Binding" enter slack value to $2$ decimal places or leave cells blank.