Consider the following LP problem.

Maximize z =3 x1+2 x2,

Subject to

Constraint 1: 2x1+3x2<=40,

Constraint 2: 3x1+ x2<=30,

Constraint 3: x1,x2>=0,

where x1 and x2 represent the decision variables. Solve the LP problem to answer the following questions.

What are the values of x1 and x2 at the optimal solution? What is the maximum value of z?

Note: Round your answers to 2 decimal places.

Value of x1 at the optimal solution ___________

Value of x2 at the optimal solution ___________

Maximum value of z ___________

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.

Constraint 1_________________________________

Constraint 2_________________________________

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

Note: If the answer to constraints is "Binding" enter the "Shadow price" and "Range of feasibility" to 2 decimal places or leave cells blank.

Shadow Price Range of Feasibility

From To

Constraint 1______________________________________

Constraint 2______________________________________

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

Note: Round your answers to 2 decimal places.

Range of Optimality for

the objective function coefficients

From To

x1____________________________ x2____________________________