Consider the following LP problem.

Maximize $z=3x_1+2x_2,$

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 $z?$

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

c$.$ Report the shadow price and range of feasibility of each binding constraint.

d$.$ What is the range of optimality for the two objective function coefficients?

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