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.
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Midterm
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
2
240
300
Upper Limit
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
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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
s.t.
5X + 3Y
2X + 3Y
2X + 5Y
6X - 5Y
X, Y
<
<
<
>
30
40
0
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)
1
2
Labour Available:
A
B
C
Profit Contribution
per unit
1.00
0.30
0.20
$30.00
100
36
50
0.35
0.20
0.50
$15.00
What is the linear model that will determine the optimal production quantities of product
1 and 2?
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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
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MGTC 74: Analysis for Decision Making - Mid-term Exam
Name: ____________________________
Student Number: __________________
 Please use pen and place “0” around choice.
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
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Do not use whiteout.
Midterm
1-c
2-b
3-d
4-c
5-d
6-a
7-d
8-b
9-c
10-b
11-2
20
15
10
5
0
0
5
X
10
Y
5
2
2
6
5
Sol: z=43
15
20
Sol
3
3
5
-5
6
43
28
40
0
S/S
30
40
0
2
0
0
(X,Y) = (5,6) slack = 2, 0 and 0
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12-2 #2
Let x1 = units of product 1 produced
x2 = units of product 2 produced
Max
s.t.
30x1
+
15x2
x1
0.30x1
0.20x1
+
+
+
0.35x2
0.20x2
0.50x2



100
36
50
Dept. A
Dept. B
Dept. C
x 1, x 2  0
13-3
500
A
X
300
Y
300
Z
300
2
3
5
9
400
B
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10
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Midterm