Consider the following problem

Maximize Z=3x1+x2

Subject to

6x1 + 3x2 ≤ 25

3x1 + 4x2 ≤ 20

x1, x2 ≥ 0

a) Solve the model using the simplex algorithm. What are the basic and nonbasic variables in the optimal solution? What are their values?

b) Answer the following questions (if possible without reoptimizing):

• How does the value of optimal basic variables change if the right-hand side of constraint 1 is changed to 10?

• How does the value of optimal basic variables change if the right-hand side of constraint 2 is changed to 10?

• How does the set of optimal basic variables change if the objective coefficient of the first variable is changed to 2?

• How does the set of optimal basic variables change if the objective coefficient of the second variable is changed to 3?