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. When the value of the output cannot be determined even if the value of the controllable input is known, the model is

a. analog.

b. digital.

c. stochastic.

d. deterministic.

2. Slack

a. is the difference between the left and right sides of a constraint.

b. is the amount by which the left side of a < constraint is smaller than the right side.

c. is the amount by which the left side of a constraint is larger than the right side.

d. exists for each variable in a linear programming problem.

3. To find the optimal solution to a linear programming problem using the graphical

method

a. find the feasible point that is the farthest away from the origin.

b. find the feasible point that is at the highest location.

c. find the feasible point that is closest to the origin.

d. None of the alternatives is correct.

4. A constraint with a positive slack value

a. will have a positive dual price.

b. will have a negative dual price.

c. will have a dual price of zero.

d. has no restrictions for its dual price.

5. A section of output from The Management Scientist is shown here.

Constraint Lower Limit Current Value Upper Limit

2 240 300 420

What will happen if the right-hand-side for constraint 2 increases by 200?

a. Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same.

b. The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.

c. The same decision variables will be positive, but their values, the objective function value, and the dual prices will change.

d. The problem will need to be resolved to find the new optimal solution and dual price.

6. Let Pij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units,

a. P13 - P14 100; P14 - P13 100

b. P13 - P14 100; P13 - P14 100

c. P13 - P14 100; P14 - P13 100

d. P13 - P14 100; P14 - P13 100

7. Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is

a. Max 2M + 3B

b. Min 4000 (M + B)

c. Max 8000M + 12000B

d. Min 2M + 3B

8. The problem which deals with the distribution of goods from several sources to several destinations is the

a. network problem

b. transportation problem

c. assignment problem

d. transshipment problem

9. The difference between the transportation and assignment problems is that

a. total supply must equal total demand in the transportation problem

b. the number of origins must equal the number of destinations in the transportation problem

c. each supply and demand value is 1 in the assignment problem

d. there are many differences between the transportation and assignment problems

10. Constraints in a transshipment problem

a. correspond to arcs.

b. include a variable for every arc.

c. require the sum of the shipments out of an origin node to equal supply.

d. All of the alternatives are correct.

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

graph and slack/surplus values.

Max 5X + 3Y

s.t. 2X + 3Y 30

2X + 5Y 40

6X - 5Y 0

X , Y 0

12. The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labour availability, labour utilization, and product profitability:

Department: Product (hours/unit) Labour Available:

1 2

A 1.00 0.35 100

B 0.30 0.20 36

C 0.20 0.50 50

Profit Contribution $30.00 $15.00

per unit

What is the linear model that will determine the optimal production quantities of product 1 and 2?

13. Draw the network for this LP problem.

Min 2XAX + 3XAY + 5XAZ+ 9XBX + 12XBY + 10XBZ

s.t. XAX + XAY + XAZ 500

XBX + XBY + XBZ 400

XAX + XBX = 300

XAY + XBY = 300

XAZ + XBZ = 300

Xij 0

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-c

2-b

3-d

4-c

5-d

6-a

7-d

8-b

9-c

10-b

11-2

X / Y / Sol
5 / 3 / 43 / S/S
2 / 3 / 28 / 30 / 2
2 / 5 / 40 / 40 / 0
6 / -5 / 0 / 0 / 0
5 / 6

Sol: z=43 (X,Y) = (5,6) slack = 2, 0 and 0

12-2 #2

Let x1 = units of product 1 produced

x2 = units of product 2 produced

Max / 30x1 / + / 15x2
s.t.
x1 / + / 0.35x2 / £ / 100 / Dept. A
0.30x1 / + / 0.20x2 / £ / 36 / Dept. B
0.20x1 / + / 0.50x2 / £ / 50 / Dept. C

x1, x2 ³ 0

13-3

MGTC 74 W07 Page 7 of 5 Midterm