University of Northern British Columbia - Business Program s1

MGTC 74: Analysis for Decision Making

Midterm Exam – Winter 07 – February 27

Chapters 1,2,3,4 and 7

Instructions:

1. Please detach the answer page for the multiple choice questions and indicate best

answer. Make sure your name is on the answer page and include it with the exam

book.

2. Answer the quantitative questions in the exam book provided only. Clearly number

each question. If you choose to use pencil then your exam cannot be

considered for re-marking.

3. Each multiple choice question is worth 2 1/2 marks for a total of 25 marks.

4. Each quantitative question is worth 25 marks for a total of 75 Marks.

5. Time allowed is 1 hour and 30 minutes.

6. Turn off all cell phones and radio frequency devices.

7. Please sign out when you leave the exam.

1. A model that uses a system of symbols to represent a problem is called

a. mathematical.

b. iconic.

c. analog.

d. constrained.

2. The improvement in the value of the objective function per unit increase in a right-

hand side is the

a. sensitivity value.

b. dual price.

c. constraint coefficient.

d. slack value.

3. Which of the following statements is NOT true?

a. A feasible solution satisfies all constraints.

b. An optimal solution satisfies all constraints.

c. An infeasible solution violates all constraints.

d. A feasible solution point does not have to lie on the boundary of the feasible region.

4. The amount by which an objective function coefficient can change before a

different set of values for the decision variables becomes optimal is the

a. optimal solution.

b. dual solution.

c. range of optimality.

d. range of feasibility.

5. The dual price measures, per unit increase in the right hand side,

a. the increase in the value of the optimal solution.

b. the decrease in the value of the optimal solution.

c. the improvement in the value of the optimal solution.

d. the change in the value of the optimal solution.

6. Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then

a. B 5

b. A - .5B + C 0

c. .5A - B - .5C 0

d. -.5A + .5B - .5C 0

7. Media selection problems usually determine

a. how many times to use each media source.

b. the coverage provided by each media source.

c. the cost of each advertising exposure.

d. the relative value of each medium.

8. The parts of a network that represent the origins are

a. the axes

b. the flow

c. the nodes

d. the arrows

9. The assignment problem constraint x31 + x32 + x33 + x34 2 means

a. agent 3 can be assigned to 2 tasks.

b. agent 2 can be assigned to 3 tasks.

c. a mixture of agents 1, 2, 3, and 4 will be assigned to tasks.

d. there is no feasible solution.

10. In a transshipment problem, shipments

a. cannot occur between two origin nodes.

b. cannot occur between an origin node and a destination node.

c. cannot occur between a transshipment node and a destination node.

d. can occur between any two nodes.

11. Find the complete optimal solution to this linear programming problem

including graph and slack/surplus values.

Min 3X + 3Y

s.t. 12X + 4Y 48

10X + 5Y 50

4X + 8Y 32

X , Y 0

12. Peter and Daughters Inc. manufacturers two products used in the fragrance industry. Both products require manufacturing operations in two departments. The following are the production time (in hours) and profit contribution figures for the two products:

Product: Profit per Unit: Labour Hours:

Dept A: Dept B:

1 25$ 6 12

2 20$ 8 10

For the coming production period, Peter has available a total of 900 hours of labour that can be allocated to either of the two departments. What is linear model that will provide the production plan and labour allocation in each department that will maximize the total contribution to profit?

13. Show both the network and the linear programming model for this assignment problem.

MGTC 74: Analysis for Decision Making - Mid-term Exam

Name: ______Student Number: ______

F Please use pen and place “0” around choice. Do not use whiteout.

1. a b c d

2. a b c d

3. a b c d

4. a b c d

5. a b c d

6. a b c d

7. a b c d

8. a b c d

9. a b c d

10. a b c d

1-a

2-b

3-c

4-c

5-c

6-d

7-a

8-c

9-a

10-d

11-4.

The complete optimal solution is X = 4, Y = 2, Z = 18, S1 = 8, S2 = 0, S3 = 0

12-3 #6

Let x1 = units of product 1

x2 = units of product 2

b1 = labor-hours Dept. A

b2 = labor-hours Dept. B

x1, x2, b1, b2 ³ 0

13-4

Let Xij = 1 if person i is assigned to job j

= 0 otherwise

Min 9X1A + 5X1B + 4X1C + 2X1D

+ 12X2A + 6X2B + 3X2C + 5X2D

+ 11X3A + 6X3B + 5X3C + 7X3D

s.t. X1A + X1B + X1C + X1D 1

X2A + X2B + X2C + X2D 1

X3A + X3B + X3C + X3D 1

X4A + X4B + X4C + X4D 1

X1A + X2A + X3A + X4A = 1

X1B + X2B + X3B + X4B = 1

X1C + X2C + X3C + X4C = 1

X1D + X2D + X3D + X4D = 1

MGTC 74 W07 Page 1 of 5 Midterm