Consider the following Linear Programming problem.

Maximize z=3x1+2x2 Subject to: Constraint 1: 3x1+x2≤30

Constraint 2: 2x1+ 3x2≤40

Constraint 3: x1, x2≥0

Where x1 and x2 represent the decision variables, Solve the LP problem, using R to answer the following questions: What are the values of x1 and x2 at the optimal solutions?

What is the maximum value of z? Identify the binding and nonbinding constraints and report the slack value, if applicable.

Report the shadow price and range of feasibility of each binding constraint. What is the range of optimality for the two objective function coefficients?