IEOPER1 Quiz 3

Question 1

In dual simplex method, what are the questions you must ask after every iteration?

Answer 1

Is the solution feasible?
Does the solution follow optimality conditions?

Question 2

True or False. You can use dual simplex even though the given model is primal or dual as long as there is a greater than or equal to (>=) sign in at least one of the constraints

Answer 2

True

Question 3

You can only use dual simplex method if the first iteration or initial tableau is ________

Answer 3

Super optimal

Question 4

if the first iteration is not super-optimal using dual simplex method, you have to _________

Answer 4

Add a redundant constraint wherein it is the sum of variables (qualify as EV) <= M.

Question 5

Guess the characteristic of the basic solution:
Is the solution feasible? Yes
Does the solution meet optimality conditions? Yes

Answer 5

Optimal

Question 6

Guess the characteristic of the basic solution:
Is the solution feasible? No
Does the solution meet optimality conditions? Yes

Answer 6

Super-optimal

Question 7

Guess the characteristic of the basic solution:
Is the solution feasible? Yes
Does the solution meet optimality conditions? No

Answer 7

Sub-optimal

Question 8

Guess the characteristic of the basic solution:
Is the solution feasible? No
Does the solution meet optimality conditions? No

Answer 8

Neither

Question 9

In converting primal model to dual model, if the primal model is a max problem, then its constraints must be ________

Answer 9

<=

Question 10

In converting primal model to dual model, if the primal model is a min problem, then its constraints must be ________

Answer 10

> =

Question 11

Primal Model : xn
Dual Model: ?

Answer 11

Tn

Question 12

Primal Model: Sn
Dual Model: ?

Answer 12

Yn

Question 13

True or False. When the iteration of a primal problem is sub-optimal, the corresponding iteration of the dual is super-optimal.

Answer 13

True

Question 14

True or False. If the shadow price of a resource is zero, then it follows that the corresponding slack variable is basic in the optimal tableau.

Answer 14

False

Question 15

True or False. The number of structural constraints in the primal is the same as the number of decision variables in the dual, and the number of decision variables in the primal is the same as the number of structural constraints in the dual.

Answer 15

True

Question 16

True or False. An unrestricted variable in the primal is converted into symmetric form by expressing it as the sum of two non-negative variables.

Answer 16

False

Question 17

True or False. The symmetric form of a primal LP model is needed to formulate its dual model whereas the standard form is needed to begin the solution process.

Answer 17

False

Question 18

True or False. The dual simplex method is used to solve for the new optimal solution if an objective function coefficient is changed beyond its allowable range of values.

Answer 18

False

Question 19

True or False. A new constraint added to an existing LP model may affect the current optimal solution mix.

Answer 19

False

Question 20

True or False. Changing the right-hand side value of a constraint will definitely change the optimal value of the objective function.

Answer 20

False

Question 21

True or False. An equality constraint in the asymmetric form of the primal guarantees that there will also be an equality constraint in the corresponding asymmetric form of the dual.

Answer 21

False

Question 22

True or False. If the shadow price of a resource is positive, the resource must necessarily be scarce.

Answer 22

True

Question 23

True or False. The dual of the dual is the primal.

Answer 23

True

Question 24

True or False. If a decision variable is non-basic in the optimal tableau, it is possible that the decision variable becomes an optimal basic decision variable if its cost per unit is increased.

Answer 24

False

Question 25

True or False. Changing the OFC of a non-basic variable will change the current optimal value of the objective function.

Answer 25

False

Question 26

True or False. If the primal problem has no feasible solution, then it necessarily follows that the dual will have no feasible solution.

Answer 26

False

Question 27

True or False. In the dual simplex method, if none of the constraint coefficients associated with the leaving variable row are negative, then the LP has an unbounded solution space.

Answer 27

True