*Please answer h. a-g are included for reference.*

4.4-3. Consider the following problem.

Maximize Z = 2x₁ + x₂,

subject to

x₁ + x₂ = 40

4x₁ + x₂ = 100

and

x₁ >= 0, x₂ >= 0.

(a) Solve this problem graphically in a freehand manner. Also identify all the CPF solutions.

(b) Now use IOR Tutorial to solve the problem graphically.

(e) Use hand calculations to solve this problem by the simplex method in tabular form.

(f) Now use IOR Tutorial to solve this problem interactively by the simplex method in tabular form.

(g) Use a software package based on the simplex method to solve the problem.

(h) Using the optimal solution and the optimal tableau, identify the binding (active) constraints at the optimal solution, the values of the shadow prices of the two rhs, and the reduced costs of the two original variables x₁ and x₂.