Optimization Exam 2

Question 1

Use this when you cannot obtain initial bfs directly.

Answer 1

Big M Method

Question 2

In the original problem, if there exists equality constraint, and there is no one variable
only appears in this constraint use this. Or
in some constraint, if there exists excess variable (-1 is its coefficient), and there is no one variable only appears in this constraint use this.

Answer 2

Artificial Variables

Question 3

If there is no non-basic variables with zero coefficient in row 0 of the optimal tableau, then the LP is:

Answer 3

Unique Solution

Question 4

In an optimal tableau, there exists an NBV with coefficient zero in row 0, and continuing the simplex algorithm will obtain another optimal tableau with a different solution:

Answer 4

Multiple Optimal Solutions

Question 5

Detected in the simplex method when an artificial variable remains positive in the final tableau.

Answer 5

Infeasible LP

Question 6

Occurs when a variable with a negative coefficient in row 0 has a nonpositive coefficient in each constraint.

Answer 6

Unbounded LP

Question 7

If an LP has at least one BFS in which a basic variable is equal to zero.

Answer 7

Degenerate LP

Question 8

What should x <= 0 be changed to?

Answer 8

-x’ >=0

Question 9

What should x urs be changed to?

Answer 9

x’ - x’’ >=0

Question 10

What’s the problem with a degenerate LP?

Answer 10

It may cycle and be infinite.

Question 11

Why do we add M?

Answer 11

Since M is a very large number, it can guarantee that the solution is equal to the original optimal solution.

Question 12

In an optimal tableau, are the coefficients for non-basic variables in row 0 Optimality or Feasibility?

Answer 12

Optimality

Question 13

In an optimal tableau, are the values for basic variables (rhs) Optimality or Feasibility?

Answer 13

Feasibility