1. If we wich to select a location for a new manufacturing plant, the best approach would be to use

A. Zero-one integer programming.

B. Mixed-integer programming.

C. A goal programming model.

D. An assignment model.

2. The shortest-route technique might be used for

A. Plan the routes for a vacation driving tour.

B. Design roads that would limit the flow of traffic through an area.

C. Find the most scenic route for a trip on spring break.

D. Connecting all the points of a network together while minimizing the number of pathways

3

Table 10-1

To==> 1 2 3 Supply

From A 20 20 40

20*3+20*6+30*4+20*7+10*6

500

B 30 30

C 20 10 30

Demand 20 70 10

What is the total cost represented by the solution shown in Table 10-1?

A. 60

B. 2500

C. 2600

D. 500

4. All the nodes must be connected in which of the following techniques?

A. Shortest-route

B. Maximal-flow

C. Minimal-spanning tree

D. All of the above

5. A company must assign mechanics to each of four jobs. The time involved according to individual

abilities. Table 10-2 shows how many minutes it takes each mechanic to perform each job. This was

solved using the Hugarian method. Table 10-3 shows the solution.

TABLE 10-2

JOB

1 2 3 4

WORKER A 4 6 5 4

B 3 5 4 7

C 5 6 5 4

D 7 5 5 6

TABLE 10-3

JOB

FINAL TABLE 1 2 3 4

WORKER A 0 1 0 0

B 0 1 0 4

C 1 1 0 0

D 3 0 0 2

If optimal assignments are made, how many total minutes are needed to complete the jobs?

A. 0

B. 4

C. 17

D. 20

4. All the nodes must be connected in which of the following techniques?

A. Shortest-route

B. Maximal-flow

C. Minimal-spanning tree

D. All of the above

5. A compnay must assign mechanics to each of four jobs. The time involved varies according to

individual abilities. Table 10-2 show how many minutes it takes each mechanic to perform each job.

This was solved using the Hungarian method. Table 10-3 shows the solution.

TABLE 10-2

JOB

1 2 3 4

WORKER A 4 6 5 4

B 3 5 4 7

C 5 6 5 4

D 7 5 5 6

TABLE 10-3

JOB

FINAL TABLE 1 2 3 4

WORKER A 0 1 0 0

B 0 1 0 4

C 1 1 0 0

D 3 0 0 2

If optimal assignments are made, how many total minutes are needed to complete the jobs?

A. 0

B. 4

C. 17

D. 20

6

Table 10-1

To==> 1 2 3 Supply

From A 20 20 40

B Start 30 30

C 20 10 30

Demand 20 70 10

What is the value of the improvement index for cell B1 shown in Table 10-1?

A. -50

B. +3

C. +2

D. +1

7. If your goal was to construct a network in which all points were connected and the distance

between them was as short as possible, which technique would you use?

A. Shortest-route

B. Maximal-flow

C. Minimal-spanning tree

D. Goal programming

8. The first step in the maximal-flow technique is to

A. Pick the node with the maximum flow.

B. Pick any path with some flow

C. Eliminate any node that has a zero flow.

D. Add a dummy flow from the start to the finish.

9. Assignment problems solved previously by linear programming techniques are also example of

A. Pure-integer programming problems

B. Mixed-integer programming problems.

C. Zero-one integer programming problems.

D. Goal programming problems.

10. A company must assign mechanics to each of four jobs. The time involved varies according to

individual abilities. Table 10-2 shows how many minutes it takes each mechanic to perform each job.

This was solved using the Hungarian method. Table 10-3 show the solution.

TABLE 10-2

JOB

1 2 3 4

WORKER A 4 6 5 4

B 3 5 4 7

C 5 6 5 4

D 7 5 5 6

TABLE 10-3

JOB

FINAL TABLE 1 2 3 4

WORKER A 0 1 0 0

B 0 1 0 4

C 1 1 0 0

D 3 0 0 2

According to Table 10-3, which is the final table for an assignment problem, which workers should be

assigned to Job 1?

A. Either worker A or worker B.

B. Only worker A could be assigned to Job 1

C. Only worker B could be assigned to Job 1

D. Any of the workers

11. The branch and bound method is often used when

A. Solving integer programming problems

B. The problem cannot be graphically solved.

C. There are fewer than three variables.

D. Computer facilities are not available.

12. When using shortest-route techniques, the first step is to

A. Connect the nearest node that minimizes the total distance to the orgin.

B. Trace the path from the warehouse to the plant.

C. Determine the average distance traveled from source to end.

D. Find the nearest node to the orgin and put a distance box by the node.

13. A mathematical programming model that permits decision makers to set and proritize multiple

objective functions is called a

A. Pure-integer programming problem.

B. Mixed-integer programming problem.

C. Zero-one integer programming problem.

D. Goal programming problem.

14. In a goal programming problem with two goals at the same priority level, all the deviational

variables are equal to zero in the optimal solution. This means

A. There is no feasible solution to the problem.

B. All goals are fully achieved.

C. Nonlinear programming must be used to solve this.

D. This problem was an integer programming problem.

15. The only restriction we place on the initial solution of a transporation problem is:

A. We must have nonzero quantities in a majority of the boxes.

B. All constraints must be satisfied.

C. Demand must be less than supply.

D. We must have a number (equal to the number of rows plus the number of columns minus

one) of boxes that contain nonzero quantities.

16. The maximal-flow technique might be used to

A. Plan the route for a school bus.

B. Adesign the traffic appraches to an airport.

C. Design roads that would limit the flow of traffic through an area.

D. Plan the routes for a vaction driving tour.

17. Which of the following techniques can be used for moving from an initial feasible solution to an

optimal solution in a transportation problem?

A. Stepping-stone method

B. Northwest corner rule

C. Vogel’s approximation method

D. Integer programming

18. A model containing a linear objective function and linear constraints but requiring that one or more

of the decision variables take on an integer value in the final solution is called

A. An integer programming problem.

B. A goal programming problem.

C. A nonlinear programming problem.

D. A multiple objective LP problem.

19. An integer programming (Maximization) problem was first solved as a linear programming problem,

and the objective function value (profit) was $253.67. The two decision variables (X, Y) in the problem

has values of X = 12.45 and Y = 32.75. If there is a single optimal solution, which of the following

must be true for the optimal integer solution to this problem?

A. X = 12 Y = 32

B. X = 12 Y = 33

C. The objective function value must be less than $253.67

D. The objective function value will be greater than $253.67

20. In the transportation problem, using the stepping stone method,

A. You must not skip over an empty cell

B. You may skip over a used cell

C. Your path may not cross over itself

D. If you have an optimus solution and get an improvement index of zero, there is another

optimum solution

This posting contains answers to following MCQs.