71) Find the shortest route from Node 1 to Node 5. From Node To Node Di
admin
71) Find the shortest route from Node 1 to
Node 5.
From
Node
To
Node
Distance
1
2
250
1
3
150
1
4
200
2
3
50
2
4
150
3
4
150
3
5
100
2
5
150
A) 200
B) 350
C) 250
D) 450
E) None of the above
72) Find the shortest route from Node 1 to
Node 6.
From
Node
To
Node
Distance
1
2
150
1
3
200
2
3
100
2
4
200
2
5
50
3
4
350
3
5
300
4
6
100
5
6
100
A) 300
B) 450
C) 550
D) 650
E) None of the above
73) Given the following traffic flows, in
hundreds of cars per hour, what is the maximum traffic flow from City 1 to City
7?
From
City
To
City
Flow
1
1
2
4
2
1
3
8
3
1
5
5
4
2
1
0
5
2
4
3
6
2
5
3
7
3
1
0
8
3
5
3
9
3
6
1
10
4
2
3
11
4
5
3
12
4
7
4
13
5
1
1
14
5
2
0
15
5
3
2
16
5
4
0
17
5
6
1
18
5
7
5
19
6
3
1
20
6
5
4
21
6
7
1
22
7
4
2
23
7
5
1
24
7
6
0
A) 1200
B) 1400
C) 900
D) 800
E) None of the above
74) Solve the minimal-spanning tree
problem defined below:
Branch
Start
Node
End
Node
Cost
1
1
3
5
2
1
2
1
3
2
4
3
4
2
5
4
5
3
4
6
6
4
6
2
A) total cost = 13
B) total cost = 15
C) total cost = 17
D) total cost = 11
E) None of the above
75) Find the shortest route from Node 1 to
Node 6.
From
Node
To
Node
Distance
1
1
2
100
2
1
4
215
3
2
3
70
4
2
4
200
5
2
5
110
6
3
4
320
7
4
5
200
8
4
6
200
9
5
6
200
A) total distance = 350
B) total distance = 410
C) total distance = 270
D) total distance = 520
E) None of the above
76) Given the following traffic flows, in
hundreds of cars per hour, what is the maximum traffic flow from Town 1 to Town
7?
From
Town
To
Town
Flow
1
1
2
4
2
1
3
7
3
1
5
9
4
2
1
0
5
2
4
3
6
2
5
5
7
3
1
1
8
3
5
3
9
3
6
4
10
4
2
3
11
4
5
1
12
4
7
0
13
5
1
1
14
5
2
0
15
5
3
3
16
5
4
0
17
5
6
5
18
5
7
1
19
6
3
1
20
6
5
6
21
6
7
3
22
7
4
5
23
7
5
2
24
7
6
0
A) max flow = 4 units
B) max flow = 6 units
C) max flow = 3 units
D) max flow = 9 units
E) None of the above
77) Find the shortest route from Node 6 to
Node 1.
Branch
From
Node
To
Node
Distance
1
1
2
150
2
1
3
200
3
2
3
100
4
2
4
200
5
2
5
50
6
3
4
350
7
3
5
300
8
4
6
100
9
5
6
100
A) branches 9, 7, and 2
B) branches 8, 6, and 2
C) branches 8, 6, 7, and 1
D) branches 9, 5, and 1
E) None of the above
78) Given the pipeline fluid flows
indicated below, determine the maximum flow from Node 1 to Node 5.
From
Node
To
Node
Fluid
Flow
1
1
2
300
2
2
1
0
3
1
3
0
4
3
1
150
5
1
4
200
6
4
1
200
7
1
5
100
8
5
1
100
9
2
4
200
10
4
2
200
11
3
4
250
12
4
3
300
13
3
5
300
14
5
3
250
15
4
5
100
16
5
4
0
A) 250
B) 300
C) 350
D) 450
E) None of the above
79) Find the
least amount of cable that will allow Jack’s Cable Company to connect the
following nodes (houses).
From
Node
To
Node
Distance
1
2
250
1
3
150
1
4
400
2
3
50
2
4
100
3
4
200
A) 250
B) 400
C) 350
D) 300
E) None of the above
80) Given the following nodes and
distances, determine the minimum length of cable necessary to connect all six
nodes.
From
Node
To
Node
Distance
1
1
2
150
2
1
3
200
3
2
3
100
4
2
4
200
5
2
5
50
6
3
4
350
7
3
5
300
8
4
6
100
9
5
6
100
A) 200
B) 300
C) 400
D) 500
E) None of the above
81) Given the following nodes and
distances, determine the minimal length of cable necessary to connect all
nodes, using Node 2 as the starting point.
From
To
Distance
1
1
2
200
2
1
3
300
3
1
5
400
4
2
3
300
5
2
4
400
6
3
4
200
7
3
5
200
8
4
5
100
9
4
6
300
10
5
6
400
A) 1200
B) 1100
C) 900
D) 700
E) None of the above
82) A certain firm has four different
operations that must be assigned to four locations. The profit (in thousands of
dollars) associated with each operation at each location is presented below.
The firm’s vice president would like to assign the various operations so that
the total profit is maximized. Find the appropriate assignments.
.jpg”>
83) Four projects must be completed, and
each of four employees will be assigned to work on exactly one of the four
projects. The table below presents an estimate of the cost that each employee
would incur if working on the respective projects. What is the minimum-cost
assignment of workers to projects?
.jpg”>
84) SE Appliances manufacturers
refrigerators in Richmond, Charlotte, and Atlanta. Refrigerators then must be
shipped to meet demand in Washington, New York, and Miami. The table below
lists the shipping costs, supply, and demand information.
.jpg”>
How many units should be shipped from each
plant to each retail store in order to minimize shipping costs?
85) Neki Sports Company manufactures
treadmills in factories located in Pittsburgh and Kansas City. These are
shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia.
Ultimately they are delivered to supply houses in New York and Los Angeles. The
available supplies at the factories, demands at the final destinations, and
shipping costs are illustrated in the table below.
.jpg”>
Formulate this problem as a linear
program.
86) Neki Sports Company manufactures
treadmills in factories located in Pittsburgh and Kansas City. These are
shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia.
Ultimately they are delivered to supply houses in New York and Los Angeles. The
available supplies at the factories, demands at the final destinations, and
shipping costs are illustrated in the table below.
.jpg”>
Determine how many units should be shipped
for all possible origin and destination points (final or intermediate) in the
distribution network in order to minimize shipping costs.
87) Find the shortest route from Node 1 to
each of the other nodes in the transportation network represented below.
Route
from
Node
Distance
1
to 2
50
1
to 3
100
2
to 3
75
2
to 4
65
3
to 4
80
3
to 5
70
4
to 5
65
4
to 6
200
5
to 6
130
88) As part of the planning for a major
office development project, it is necessary to install telephone line to the
buildings. Information about the project is given below. The distances are
provided in hundreds of feet. Which offices should be connected so that total
wiring costs (i.e., total distance) are minimized? What is the total length of
this?
Building
Distances
(100s ft)
1
to 2
4
1
to 4
3
2
to 3
2
2
to 4
4
3
to 5
1
3
to 6
5
4
to 5
3
4
to 7
3
5
to 7
2
6
to 7
6
89) A cable company must provide service
for 7 houses in a particular neighborhood. They would like to wire the
neighborhood in a way to minimize the wiring costs (or distance). How should
the cable company wire the neighborhood and what would be the minimal length of
the network?
House
Distances
(yards)
1
to 2
100
1
to 3
400
1
to 4
300
2
to 3
300
2
to 4
250
2
to 5
400
3
to 5
350
3
to 6
450
4
to 5
300
4
to 7
250
5
to 7
100
6
to 7
150
90) Given a network with the following
distances:
From
Node
To
Node
Distance
1
2
4
1
3
1
2
3
2
2
4
3
3
4
6
3
5
3
3
6
9
4
5
7
5
6
5
(a) Determine which nodes should be
connected to get the minimum distance from Nodes 1 through 6.
(b) Determine the minimum distance.71) Find the shortest route from Node 1 to
Node 5.FromNodeToNodeDistance122501315014200235024150341503510025150A) 200B) 350C) 250D) 450E) None of the above72) Find the shortest route from Node 1 to
Node 6.FromNodeToNodeDistance12150132002310024200255034350353004610056100A) 300B) 450C) 550D) 650E) None of the above73) Given the following traffic flows, in
hundreds of cars per hour, what is the maximum traffic flow from City 1 to City
7?From
CityTo
CityFlow112421383155421052436253731083539361104231145312474135111452015532165401756118575196312065421671227422375124760A) 1200B) 1400C) 900D) 800E) None of the above74) Solve the minimal-spanning tree
problem defined below:BranchStart
NodeEnd
NodeCost113521213243425453466462A) total cost = 13B) total cost = 15C) total cost = 17D) total cost = 11E) None of the above75) Find the shortest route from Node 1 to
Node 6.FromNodeToNodeDistance11210021421532370424200525110634320745200846200956200A) total distance = 350B) total distance = 410C) total distance = 270D) total distance = 520E) None of the above76) Given the following traffic flows, in
hundreds of cars per hour, what is the maximum traffic flow from Town 1 to Town
7?From
TownTo
TownFlow112421373159421052436255731183539364104231145112470135111452015533165401756518571196312065621673227452375224760A) max flow = 4 unitsB) max flow = 6 unitsC) max flow = 3 unitsD) max flow = 9 unitsE) None of the above77) Find the shortest route from Node 6 to
Node 1.BranchFromNodeToNodeDistance11215021320032310042420052550634350735300846100956100A) branches 9, 7, and 2B) branches 8, 6, and 2C) branches 8, 6, 7, and 1D) branches 9, 5, and 1E) None of the above78) Given the pipeline fluid flows
indicated below, determine the maximum flow from Node 1 to Node 5.FromNodeToNodeFluidFlow1123002210313043115051420064120071510085110092420010422001134250124330013353001453250154510016540A) 250B) 300C) 350D) 450E) None of the above79) Find the
least amount of cable that will allow Jack’s Cable Company to connect the
following nodes (houses).FromNodeToNodeDistance12250131501440023502410034200A) 250B) 400C) 350D) 300E) None of the above80) Given the following nodes and
distances, determine the minimum length of cable necessary to connect all six
nodes.FromNodeToNodeDistance11215021320032310042420052550634350735300846100956100A) 200B) 300C) 400D) 500E) None of the above81) Given the following nodes and
distances, determine the minimal length of cable necessary to connect all
nodes, using Node 2 as the starting point.FromToDistance1122002133003154004233005244006342007352008451009463001056400A) 1200B) 1100C) 900D) 700E) None of the above82) A certain firm has four different
operations that must be assigned to four locations. The profit (in thousands of
dollars) associated with each operation at each location is presented below.
The firm’s vice president would like to assign the various operations so that
the total profit is maximized. Find the appropriate assignments..jpg”>83) Four projects must be completed, and
each of four employees will be assigned to work on exactly one of the four
projects. The table below presents an estimate of the cost that each employee
would incur if working on the respective projects. What is the minimum-cost
assignment of workers to projects?.jpg”>84) SE Appliances manufacturers
refrigerators in Richmond, Charlotte, and Atlanta. Refrigerators then must be
shipped to meet demand in Washington, New York, and Miami. The table below
lists the shipping costs, supply, and demand information..jpg”>How many units should be shipped from each
plant to each retail store in order to minimize shipping costs?85) Neki Sports Company manufactures
treadmills in factories located in Pittsburgh and Kansas City. These are
shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia.
Ultimately they are delivered to supply houses in New York and Los Angeles. The
available supplies at the factories, demands at the final destinations, and
shipping costs are illustrated in the table below..jpg”>Formulate this problem as a linear
program.86) Neki Sports Company manufactures
treadmills in factories located in Pittsburgh and Kansas City. These are
shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia.
Ultimately they are delivered to supply houses in New York and Los Angeles. The
available supplies at the factories, demands at the final destinations, and
shipping costs are illustrated in the table below..jpg”>Determine how many units should be shipped
for all possible origin and destination points (final or intermediate) in the
distribution network in order to minimize shipping costs.87) Find the shortest route from Node 1 to
each of the other nodes in the transportation network represented below.Route
from
NodeDistance1
to 2501
to 31002
to 3752
to 4653
to 4803
to 5704
to 5654
to 62005
to 613088) As part of the planning for a major
office development project, it is necessary to install telephone line to the
buildings. Information about the project is given below. The distances are
provided in hundreds of feet. Which offices should be connected so that total
wiring costs (i.e., total distance) are minimized? What is the total length of
this?BuildingDistances
(100s ft)1
to 241
to 432
to 322
to 443
to 513
to 654
to 534
to 735
to 726
to 7689) A cable company must provide service
for 7 houses in a particular neighborhood. They would like to wire the
neighborhood in a way to minimize the wiring costs (or distance). How should
the cable company wire the neighborhood and what would be the minimal length of
the network?House
Distances
(yards)1
to 21001
to 34001
to 43002
to 33002
to 42502
to 54003
to 53503
to 64504
to 53004
to 72505
to 71006
to 715090) Given a network with the following
distances:FromNodeTo
NodeDistance124131232243346353369457565(a) Determine which nodes should be
connected to get the minimum distance from Nodes 1 through 6.(b) Determine the minimum distance.
