21. What is the constraint for node 2 in the
following shortest path problem?
.png”>
a. 
X_{12}– X_{13} = 0 
b. 
X_{12}– X_{24} = 1 
c. 
X_{12} + X_{13} = 0 
d. 
X_{12} + X_{24} = 0 
22. An oil company wants to create lube oil,
gasoline and diesel fuel at two refineries. There are two sources of crude oil.
Consider arc 24. The per unit shipping cost of crude B from source 2 (node 2)
to refinery 2 (node 4) is $11 and the yield is 85 percent. The following
network representation depicts this problem. What is the balance of flow
constraint for node 3 (Refinery 1)?
.png”>
a. 
X_{13} + X_{23}– .95 X_{35}– .90 X_{36}– .90 X_{37} = 0 
b. 
.80 X_{13} + .95 X_{23}– X_{35}– X_{36}– X_{37} = 0 
c. 
.80 X_{13} + .95 X_{23}– .90 X_{36}– .90 X_{37}³ 0 
d. 
X_{13} + X_{23}– X_{35}– X_{36}– X_{37}³ 0 
23. An oil company wants to create lube oil,
gasoline and diesel fuel at two refineries. There are two sources of crude oil.
Consider arc 24. The per unit shipping cost of crude B from source 2 (node 2)
to refinery 2 (node 4) is $11 and the yield is 85 percent. The following
flowchart depicts this problem. What is the balance of flow constraint for node
7 (Diesel)?
.png”>
a. 
X_{35} + X_{36} + X_{37} = 75 
b. 
X_{37} + X_{47}³ 75 
c. 
.90 X_{37} + .95 X_{47} = 75 
d. 
X_{37} + X_{47}X_{36}– X_{35}– X_{45}– X_{46}³ 75 
24. A network flow problem that allows gains or
losses along the arcs is called a
a. 
nonconstant network flow model. 
b. 
nondirectional, shortest path model. 
c. 
generalized network flow model. 
d. 
transshipment model with linear side constraints. 
25. What is the objective function for the
following shortest path problem?
.png”>
a. 
X_{12}– X_{13} = 0 
b. 
MIN50 X_{12}– 200 X_{13} + 100 X_{24} + 35 X_{34} 
c. 
MIN 50 X_{12} + 200 X_{13} + 100 X_{24} + 35 X_{34} 
d. 
MAX50 X_{12}– 200 X_{13} + 100 X_{24} + 35 X_{34} 
26. Which formula should be used to determine the
Net Flow values in cell K6 in the following spreadsheet model?
A 
B 
C 
D 
E 
F 
G 
H 
I 
J 
K 
L 

1 

2 

3 

4 
Supply/ 

5 
Ship 
From 
To 
Unit Cost 
Nodes 
Net Flow 
Demand 

6 
55 
1 
LAV 
2 
PHO 
60 
1 
LAV 
100 
100 

7 
45 
1 
LAV 
4 
REN 
120 
2 
PHO 
50 
50 

8 
5 
2 
PHO 
3 
LAX 
160 
3 
LAX 
30 
30 

9 
0 
3 
LAX 
5 
SAN 
70 
4 
REN 
45 
45 

10 
25 
5 
SAN 
3 
LAX 
90 
5 
SAN 
90 
90 

11 
0 
5 
SAN 
4 
REN 
70 
6 
DEN 
35 
35 

12 
0 
5 
SAN 
6 
DEN 
90 
7 
SLC 
150 
150 

13 
0 
6 
DEN 
5 
SAN 
50 

14 
0 
7 
SLC 
4 
REN 
190 

15 
115 
7 
SLC 
5 
SAN 
90 

16 
35 
7 
SLC 
6 
DEN 
100 

17 

18 
Total 
25600 
a. 
SUMIF($C$6:$C$16,I6,$B$6:$B$16)SUMIF($E$6:$E$16,I6,$B$6:$B$16) 
b. 
SUMIF($I$6:$I$12,B6,$B$6:$B$16)SUMIF($I$6:$I$12,I6,$B$6:$B$16) 
c. 
SUMIF($E$6:$E$16,I6,$B$6:$B$16)SUMIF($C$6:$C$16,I6,$B$6:$B$16) 
d. 
SUMPRODUCT(B6:B16,G6:G16) 
27. Which property of network flow models
guarantees integer solutions?
a. 
linear constraints and balance of flow equation format 
b. 
linear objective function coefficients 
c. 
integer objective function coefficients 
d. 
integer constraint RHS values and balance of flow equation format 
28. In generalized network flow problems
a. 
solutions may not be integer values. 
b. 
flows along arcs may increase or decrease. 
c. 
it can be difficult to tell if total supply is adequate to meet total 
d. 
all of these. 
29. What happens to the solution of a network
flow model if side constraints are added that do not obey the balance of flow
rules?
a. 
The model solution is not guaranteed to be integer. 
b. 
The model solution will more accurately reflect reality. 
c. 
The model solution will be integer but more accurate. 
d. 
The model solution is not guaranteed to be feasible. 
30. Consider modeling a warehouse with three
inflow arcs and three outflow arcs. The warehouse node is a transshipment node
but has a capacity of 100. How would one modify the network model to avoid
adding a side constraint that limits either the sum of inflows or the sum of
the outflows to 100?
a. 
Place a limit of 34 on each inflow arc. 
b. 
Add a side constraint limiting the outflow arcs sum to 100. 
c. 
Separate the warehouse node into two nodes, connected by a single arc, 
d. 
It cannot be accomplished, a side constraint must be added. 