Quantitative Analysis Analysis for Management, 11e (Render) Chapter 11 Network Models 1) The minimal spanning tree technique fnds the shortest route to a series o destinations. Answer: FALSE i!: " Topic: #$T%&'(T#&$ -
") #n the minimal spanning tree technique technique it is necessar* to start at the last node in the networ+. Answer: FALSE i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, -
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0) The maimal 2ow technique would 3e helpul to cit* planners in determining how reewa*s should 3e epanded. Answer: T%'E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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6) The minimal spanning tree technique determines the path through the networ+ that connects all the points while minimi7ing total distance. Answer: T%'E i!: " Topic: #$T%&'(T#&$ -
8) The shortest route technique is the same as the minimal spanning tree technique. Answer: FALSE i!: 1 Topic: #$T%&'(T#&$ -
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9) /us* highwa*s are oten anal*7ed with the maimal 2ow technique. Answer: T%'E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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) Transportation companies would defnitel* 3e interested in the shortest route technique to optimi7e tra;el. Answer: T%'E i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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=) (a3le tele;ision companies would emplo* the shortest route technique to la* out the ca3les connecting indi;idual houses. Answer: FALSE i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, -
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@) 5e ma* 3egin the maimal 2ow technique 3* pic+ing an ar3itrar* path through the networ+. Answer: T%'E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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1?) The maimal 2ow technique fnds the maimum 2ow o an* quantit* or su3stance through a networ+. Answer: T%'E i!: 1 Topic: #$T%&'(T#&$ -
11) The maimal 2ow technique might 3e used 3* the '.S. Arm* (orps o Engineers to stud* water run o! in an aempt to minimi7e the danger rom 2oods. Answer: T%'E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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1") The shortest route technique might 3e used 3* someone planning a ;acation in order to minimi7e the required amount o dri;ing. Answer: T%'E i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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10) The points on the networ+ are reerred to as nodes. Answer: T%'E i!: " Topic: #$T%&'(T#&$ 16) Lines connecting nodes on a networ+ are called lin+s. Answer: FALSE i!: " Topic: #$T%&'(T#&$ 18) A tra;eling salesperson might use the shortest route technique to minimi7e the distance tra;eled to reach one o hisBher customers. Answer: T%'E i!: " Topic: S<&%TEST %&'TE -%&/LE, -
19) #n the minimal spanning tree technique i there is a tie or the nearest node that suggests that there ma* 3e more than one optimal solution. Answer: T%'E i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, -
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1) The maimal 2ow model might 3e o use to an engineer loo+ing or spare capacit* in an oil pipeline s*stem. Answer: T%'E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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1=) The shortest route model assumes that one is tr*ing t r*ing to connect two end points in the shortest manner possi3le rather than aempting to connect all the nodes in the model. Answer: T%'E i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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1@) #n the maimal 2ow technique a 7ero C?) means no 2ow or a one wa* arc. Answer: T%'E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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"?) The maimal 2ow model assumes that there is a net 2ow rom DsourceD to Dsin+.D Answer: T%'E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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"1) # *our goal was to construct a networ+ in which all points were connected and the distance 3etween them was as short as possi3le the technique that *ou would use is A) shortest route. /) maimal 2ow. () shortest spanning tree. ) minimal 2ow. E) minimal spanning tree. Answer: E i!: " Topic: #$T%&'(T#&$ -
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"") The minimal spanning technique would 3est 3e used A) to assign wor+ers to o3s in the t he cheapest manner. /) to determine LA$ networ+ wiring within a 3uilding. () to minimi7e trac 2ow on a 3us* highwa*. ) 3* a truc+ing compan* ma+ing requent 3ut repeata3le drops. E) to determine the num3er o units to ship rom each source to each destination. Answer: / i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, -
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"0) The maimal 2ow technique would 3est 3e used A) to assign wor+ers to o3s in the t he cheapest manner. /) to determine the num3er o units to ship rom each source to each destination. () to determine LA$ networ+ wiring within a 3uilding. ) to maimi7e trac 2ow on a 3us* highwa*. E) 3* a truc+ing compan* ma+ing requent 3ut repeata3le drops. Answer: i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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"6) A line in a networ+ that ma* represent a path or a route is called aCn) GGGGGGGG. A) arc /) 3ranch () line ) or+ E) sin+ Answer: A i!: 1 Topic: #$T%&'(T#&$ "8) A point in the networ+ that is at the 3eginning or end o a route is called aCn) GGGGGGGG. A) arc /) 3ranch () line ) node E) source Answer: i!: 1 Topic: #$T%&'(T#&$ "9) The fnal node or destination in a networ+ is called aCn) GGGGGGGG. A) arc /) 3ranch () source ) mouth E) sin+ Answer: E i!: 1 Topic: ,A4#,AL FL&5 -%&/LE, -
") The origin or 3eginning node in a networ+ is called GGGGGGGG. A) home /) delta () source ) mouth E) sin+ Answer: ( i!: 1 Topic: ,A4#,AL FL&5 -%&/LE, -
"=) A technique that allows a researcher to determine the greatest amount o material that can mo;e through a networ+ is called A) maimal 2ow. /) maimal spanning. () shortest route. ) maimal tree. Answer: / i!: " Topic: #$T%&'(T#&$ -
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"@) The frst step in the maimal 2ow technique is to A) pic+ the node with the maimum 2ow. /) pic+ an* path with some 2ow. () eliminate an* node that has a 7ero 2ow. ) add a dumm* 2ow rom the start to the fnish. E) $one o the a3o;e Answer: / i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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0?) The shortest route technique would 3est 3e used to GGGGGGGG A) assign wor+ers to o3s in the cheapest manner. /) determine the num3er o units to ship rom each source to each destination. () determine the amount o LA$ networ+ wiring within a 3uilding. ) minimi7e the amount o trac 2ow on a 3us* highwa*. E) determine the path or a truc+ ma+ing requent 3ut repeata3le drops. Answer: E i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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01) 5hen using the shortest route technique the frst step is to A) connect the nearest node that minimi7es the total distance to the origin. /) trace the path rom the warehouse to the plant. () determine the a;erage distance tra;eled rom source to end. ) fnd the nearest node to the origin and put a distance 3o 3* the node. E) $one o the a3o;e Answer: i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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0") The shortest route technique might 3e logicall* used or A) fnding the longest time to tra;el 3etween two points. /) fnding the shortest tra;el distance 3etween two points. () fnding the most scenic route to allow tra;el to se;eral places during a trip on spring 3rea+. ) connecting all the points o a networ+ together while minimi7ing the distance 3etween them. E) $one o the a3o;e Answer: / i!: " Topic: #$T%&'(T#&$ -
00) All the nodes must 3e connected in which o the ollowing techniquesH A) minimal 2ow /) maimal spanning tree () shortest route ) maimal 2ow E) minimal spanning tree Answer: E i!: 1 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, -
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8 (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
06) The minimal spanning tree technique would 3est 3e used A) 3* a orest ranger see+ing to minimi7e the ris+ o orest fres. /) 3* a telephone compan* aempting to la* out wires in a new housing de;elopment. () 3* an airline la*ing out 2ight routes. ) $one o the a3o;e E) All o the a3o;e Answer: / i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, -
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08) 5hich o the ollowing techniques is not discussed in (hapter 11H A) shortest route /) maimal 2ow () linear programming ) minimal 2ow E) minimal spanning tree Answer: i!: 1 Topic: IA%#&'S -
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09) The maimal 2ow technique might 3e used A) to help design the mo;ing sidewal+s transporting passengers rom one terminal to another in a 3us* airport. /) 3* someone designing the trac approaches to an airport. () 3* someone aempting to design roads that would limit the 2ow o trac through an area. ) All o the a3o;e E) $one o the a3o;e Answer: i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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0) 5hich o the ollowing pro3lems can 3e sol;ed using linear programmingH A) maimal 2ow pro3lem /) shortest route pro3lem () minimal spanning tree pro3lem ) A and / E) A / and ( Answer: i!: " Topic: IA%#&'S -
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0=) 5hich o the ollowing pro3lems can 3e sol;ed as a linear program using 3inar* decision ;aria3lesH A) maimal 2ow pro3lem /) shortest route pro3lem () minimal spanning tree pro3lem ) A and / E) A / and ( Answer: / i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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0@) 5hich o the ollowing pro3lems can 3e sol;ed as a linear program using integer decision ;aria3lesH A) maimal 2ow pro3lem /) shortest route pro3lem () minimal spanning tree pro3lem ) A and / E) A / and ( Answer: A i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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6?) The second step in the maimal 2ow technique is to A) pic+ the node with the maimum 2ow. /) pic+ an* path with some 2ow. () decrease the 2ow as much as possi3le. ) add capacit* to the path with minimum 2ow. E) fnd the arc on the pre;iousl* chosen path with the smallest 2ow capacit* a;aila3le. Answer: E i!: " Topic: ,A4#,AL FL&5 -%&/LE, -
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61) The shortest route technique would 3est 3e used to A) plan the routes or a ;acation dri;ing tour. /) plan the route or a school 3us. () determine the path or a truc+ ma+ing requent runs rom a actor* to a warehouse. ) All o the a3o;e E) $one o the a3o;e Answer: i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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6") 5hen using the shortest route technique the second step is to A) fnd the net nearest node to the origin and put the distance in a 3o 3* the node. /) trace the path rom the warehouse to the plant. () determine the a;erage distance tra;eled rom source to end. ) fnd the nearest node to the origin and put a distance 3o 3* the node. E) $one o the a3o;e Answer: A i!: " Topic: S<&%TEST %&'TE -%&/LE, -
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60) #n networ+ models the lines connecting the nodes are called GGGGGGGG. A) 3ridges /) arrows () spans ) arcs E) lin+s Answer: i!: " Topic: #$T%&'(T#&$ (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
66) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 " 1
To " 0 0
istance 0?? 18? "??
A) 68? /) 18? () 08? ) 98? E) $one o the a3o;e Answer: ( i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
68) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 1 " " 0
To " 0 0 6 6
istance "?? 0?? 08? 08? "8?
A) 1?? /) 8? () =8? ) @?? E) $one o the a3o;e Answer: / i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
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69) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 " 1 " 0 6 0
To " 6 0 0 6 8 8
istance 1?? 18? "?? 8? 18 "8? 0??
A) 1?? /) 18? () 88? ) 1""8 E) $one o the a3o;e Answer: ( i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
6) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 1 " " 1 0 0 6
To " 0 0 8 6 6 8 8
istance 1?? 8? "?? 0"8 8? 08? 6?? 68?
A) 0?? /) 8"8 () 98 ) 1@"8 E) $one o the a3o;e Answer: / i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
@ (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
6=) -ipeline 2uid 2ows are indicated 3elow. etermine the maimum 2ow rom $ode 1 to $ode 0. From $ode 1 0 1 " " 0
To $ode 0 1 " 1 0 "
Fluid Flow 6?? 1?? 0?? ? 1?? 1??
A) 1?? /) 6?? () 8?? ) ?? E) $one o the a3o;e Answer: ( i!: " Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
6@) -ipeline 2uid 2ows are indicated 3elow. etermine the maimum 2ow rom $ode 1 to $ode 6. From $ode 1 " 1 6 1 0 " 6 0 6
To $ode " 1 6 1 0 1 6 " 6 0
Fluid Flow 6?? ? "?? "?? "?? ? "?? "?? 0?? 0??
A) "?? /) 0?? () 9?? ) ?? E) $one o the a3o;e Answer: ( i!: " Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
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8?) Find the shortest route rom $ode 1 to $ode 6 using the shortest route technique. -
From $ode 1 1 " " 0
To $ode " 0 0 6 6
istance 0?? "?? 8? "8? 68?
A) 98? /) 68? () 88? ) 8?? E) =?? Answer: i!: " Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
81) Find the shortest route rom $ode 1 to $ode 6. From $ode 1 1 1 " " 0
To $ode " 0 6 0 6 6
istance "8? 6?? 9?? 8? 0?? "??
A) 8? /) 8?? () 88? ) 9?? E) 8? Answer: / i!: " Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
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8") Find the shortest route rom $ode 1 to $ode 9. From $ode 1 1 " " 6 0 0 8
To $ode " 0 6 0 9 6 8 9
istance 18? "?? "?? 8? 1?? 0?? 08? 1??
A) 0?? /) 68? () 88? ) 98? E) $one o the a3o;e Answer: / i!: " Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
80) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 " 1 " 0 6
To " 0 0 6 8 8
istance 1"? 1?? "?? 18? @? 1?
A) "@? /) 01? () 9"? ) 69? E) $one o the a3o;e Answer: i!: " Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
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86) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 1 1 " " 0 0 6 6 8
To " 0 8 0 6 6 8 8 9 9
istance "?? 0?? 6?? 0?? 6?? "?? "?? 1?? 0?? 6??
A) 1??? /) =?? () ?? ) 11?? E) $one o the a3o;e Answer: i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
88) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 1 " " " 0 0 6 6 8
To " 0 0 6 8 6 8 8 9 9
istance 1?? "?? 1?? 18? "?? 18? 0?? "8? "?? 1??
A) @?? /) 98? () 6?? ) 1"?? E) $one o the a3o;e Answer: / i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
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89) i;en the ollowing distances 3etween destination nodes what is the minimum distance that connects all the nodesH From 1 1 " " 1 0 0 0 6 6 8
To " 0 0 8 6 6 8 9 8 9 9
istance 1?? 8? "?? 0?? 8? 08? 6?? 6?? 68? 08? "??
A) @?? /) 1"?? () 11?? ) ?? E) $one o the a3o;e Answer: i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
8) -ipeline 2uid 2ows are indicated 3elow. etermine the maimum 2ow rom $ode 1 to $ode 6. From $ode 1 0 1 " " 0 0 6
To $ode 0 1 " 1 0 " 6 0
Fluid Flow "?? ? 18? 8? 1?? 1?? 18? 8?
A) 1?? /) 18? () "?? ) 8? E) $one o the a3o;e Answer: / i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
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8=) -ipeline 2uid 2ows are indicated 3elow. etermine the maimum 2ow rom $ode 1 to $ode 8. From $ode 1 " 1 0 1 6 1 8 " 6 0 6 0 8 6 8
To $ode " 1 0 1 6 1 8 1 6 " 6 0 8 0 8 6
Fluid Flow 0?? ? ? 18? "?? "?? 1?? 1?? "?? "?? "8? 0?? 0?? "8? 1?? ?
A) 0?? /) 6?? () 9?? ) 8?? E) $one o the a3o;e Answer: i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
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8@) Find the shortest route rom $ode 1 to $ode 8 using the shortest route technique. -
From $ode 1 1 " " 0 0 6
To $ode " 0 0 6 6 8 8
istance "?? 18? 8? 0?? "8? "?? 18?
A) 08? /) 6?? () 68? ) 9?? E) $one o the a3o;e Answer: A i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
9?) Find the shortest route rom $ode 1 to $ode 8. From $ode 1 1 1 " " 0 0 "
To $ode " 0 6 0 6 6 8 8
istance "8? 18? "?? 8? 18? 18? 1?? 18?
A) "?? /) 08? () "8? ) 68? E) $one o the a3o;e Answer: ( i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
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91) Find the shortest route rom $ode 1 to $ode 9. From $ode 1 1 " " " 0 0 6 8
To $ode " 0 0 6 8 6 8 9 9
istance 18? "?? 1?? "?? 8? 08? 0?? 1?? 1??
A) 0?? /) 68? () 88? ) 98? E) $one o the a3o;e Answer: A i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
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9") i;en the ollowing trac 2ows in hundreds o cars per hour what is the maimum trac 2ow rom (it* 1 to (it* H
1 " 0 6 8 9 = @ 1? 11 1" 10 16 18 19 1 1= 1@ "? "1 "" "0 "6
From (it* 1 1 1 " " " 0 0 0 6 6 6 8 8 8 8 8 8 9 9 9
To (it* " 0 8 1 6 8 1 8 9 " 8 1 " 0 6 9 0 8 6 8 9
Flow 6 = 8 ? 0 0 ? 0 1 0 0 6 1 ? " ? 1 8 1 6 1 " 1 ?
A) 1"?? /) 16?? () @?? ) =?? E) $one o the a3o;e Answer: ( i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
1= (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
90) Sol;e the minimal spanning tree pro3lem defned 3elow: -
/ranch 1 " 0 6 8 9
Start $ode 1 1 " " 0 6
End $ode 0 " 6 8 6 9
(ost 8 1 0 6 9 "
A) total cost 10 /) total cost 18 () total cost 1 ) total cost 11 E) $one o the a3o;e Answer: / i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills =
=
=
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96) Find the shortest route rom $ode 1 to $ode 9.
1 " 0 6 8 9 = @
From $ode 1 1 " " " 0 6 6 8
To $ode " 6 0 6 8 6 8 9 9
istance 1?? "18 ? "?? 11? 0"? "?? "?? "??
A) total distance 08? /) total distance 61? () total distance "? ) total distance 8"? E) $one o the a3o;e Answer: / i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills =
=
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98) i;en the ollowing trac 2ows in hundreds o cars per hour what is the maimum trac 2ow rom Town 1 to Town H
1 " 0 6 8 9 = @ 1? 11 1" 10 16 18 19 1 1= 1@ "? "1 "" "0 "6
From Town 1 1 1 " " " 0 0 0 6 6 6 8 8 8 8 8 8 9 9 9
To Town " 0 8 1 6 8 1 8 9 " 8 1 " 0 6 9 0 8 6 8 9
Flow 6 @ ? 0 8 1 0 6 0 1 ? 1 ? 0 ? 8 1 1 9 0 8 " ?
A) ma 2ow 6 units /) ma 2ow 9 units () ma 2ow 0 units ) ma 2ow @ units E) $one o the a3o;e Answer: A i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills =
=
=
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99) Find the shortest route rom $ode 9 to $ode 1.
/ranch 1 " 0 6 8 9 = @
From $ode 1 1 " " " 0 0 6 8
To $ode " 0 0 6 8 6 8 9 9
istance 18? "?? 1?? "?? 8? 08? 0?? 1?? 1??
A) 3ranches @ and " /) 3ranches = 9 and " () 3ranches = 9 and 1 ) 3ranches @ 8 and 1 E) $one o the a3o;e Answer: i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
"1 (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
9) i;en the pipeline 2uid 2ows indicated 3elow determine the maimum 2ow rom $ode 1 to $ode 8.
1 " 0 6 8 9 = @ 1? 11 1" 10 16 18 19
From $ode 1 " 1 0 1 6 1 8 " 6 0 6 0 8 6 8
To $ode " 1 0 1 6 1 8 1 6 " 6 0 8 0 8 6
Fluid Flow 0?? ? ? 18? "?? "?? 1?? 1?? "?? "?? "8? 0?? 0?? "8? 1?? ?
A) "8? /) 0?? () 08? ) 68? E) $one o the a3o;e Answer: E i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
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9=) Find the least amount o ca3le that will allow Jac+Ks (a3le (ompan* to connect the ollowing nodes Chouses). From $ode 1 1 1 " " 0
To $ode " 0 6 0 6 6
istance "8? 18? 6?? 8? 1?? "??
A) "8? /) 6?? () 08? ) 0?? E) $one o the a3o;e Answer: i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
9@) i;en the ollowing nodes and distances determine the minimum length o ca3le necessar* to connect all si nodes.
1 " 0 6 8 9 = @
From $ode 1 1 " " " 0 0 6 8
To $ode " 0 0 6 8 6 8 9 9
istance 18? "?? 1?? "?? 8? 08? 0?? 1?? 1??
A) "?? /) 0?? () 6?? ) 8?? E) $one o the a3o;e Answer: i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
"0 (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
?) i;en the ollowing nodes and distances determine the minimal length o ca3le necessar* to connect all nodes using $ode " as the starting point.
1 " 0 6 8 9 = @ 1?
From 1 1 1 " " 0 0 6 6 8
To " 0 8 0 6 6 8 8 9 9
istance "?? 0?? 6?? 0?? 6?? "?? "?? 1?? 0?? 6??
A) 1"?? /) 11?? () @?? ) ?? E) $one o the a3o;e Answer: / i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
"6 (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
1) Find the shortest route rom $ode 1 to each o the other nodes in the transportation networ+ represented 3elow. %oute rom $ode 1 to " 1 to 0 " to 0 " to 6 0 to 6 0 to 8 6 to 8 6 to 9 8 to 9
istance 8? 1?? 8 98 =? ? 98 "?? 10?
Answer:
$ode " 0 6 8 9
Shortest %oute 1" 10 1"6 108 1"689 -
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istance 8? 1?? 118 1? 01?
i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
"8 (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
") As part o the planning or a maor oce de;elopment proect it is necessar* to install telephone line to the 3uildings. #normation a3out the proect is gi;en 3elow. The distances are pro;ided in hundreds o eet. 5hich oces should 3e connected so that total wiring costs Ci.e. total distance) are minimi7edH 5hat is the total length o thisH /uilding 1 to " 1 to 6 " to 0 " to 6 0 to 8 0 to 9 6 to 8 6 to 8 to 9 to
istances C1??s t) 6 0 " 6 1 8 0 0 " 9
Answer: &ne solution is to connect 1 6 " 0 0 9 0 8 6 8 8 . Total length i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
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0) A ca3le compan* must is to pro;ide ser;ice or houses in a particular neigh3orhood. The* would li+e to wire the neigh3orhood in a wa* to minimi7e the wiring costs Cor distance).
istances C*ards) 1?? 6?? 0?? 0?? "8? 6?? 08? 68? 0?? "8? 1?? 18?
Answer: &ne solution is to connect 1 " " 0 " 6 6 8 9 . Total length i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
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"9 (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
6) i;en a networ+ with the ollowing distances: From $ode 1 1 " " 0 0 0 6 8
To $ode " 0 0 6 6 8 9 8 9
istance 6 1 " 0 9 0 @ 8
Ca) etermine which nodes should 3e connected to get the minimum distance rom $odes 1 through 9. C3) etermine the minimum distance. Answer: Ca) (onnect 1 0 8 9. C3) ,inimum distance @ i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
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8) The west to east air trac s*stem passing through the 'nited States can handle aircrat 2ows with capacities in hundreds o planes per hour as shown. 5hat is the pea+ air trac load CFrom (it* 1 to (it* 8) in aircrat per hour that this s*stem can handleH -
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Answer: %oute 1"08 can handle "?? per hour and %oute 168 can handle 0?? per hour or a total o 8?? aircrat per hour. i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
" (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
9) Find the shortest route rom $ode 1 to each o the other nodes in the transportation networ+ represented 3elow. %oute From $ode 1 to " 1 to 0 " to 0 " to 8 0 to 6 0 to 8 0 to 9 6 to 9 8 to 9
istance 8? 1?? 8 9? =? ? 98 "?? 18?
Answer: $ode " 0 6 8 9
Shortest %oute 1" 10 106 1"8 109 -
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istance 8? 1?? 1=? 11? 198
i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
"= (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
) A logistics compan* is determining the shortest route to get to a selected fnal destination. The inormation on possi3le paths and distances is gi;en 3elow: %oute From $ode 1 to " 1 to 0 1 to 6 " to 6 " to 8 0 to 6 0 to 8 6 to 8 6 to 9 8 to 9 8 to 9 to
istance 8? 1?? 1"8 8 1=? 1?? 1"8 1? "?? 1"8 1?? 8
Answer: 1 0 8 0"8 i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
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=) As part o the planning or a maor oce de;elopment proect it is necessar* to install telephone lines to the 3uildings. #normation a3out the proect is gi;en 3elow. The distances are pro;ided in hundreds o eet. 5hich oces should 3e connected so that total wiring costs Ci.e. total distance) are minimi7edH 5hat is the total length o thisH /uildings 1 to " 1 to 0 1 to 6 " to 6 0 to 8 0 to 9 6 to 8 6 to 8 to 9 to
istances C1??s t) 6 0 " 6 1 8 0 0 " 9
Answer: (onnect: 1 6 6 8 8 0 9 8 0 and either 6 " or 1 ". Total length is 1?? eet. Alternate solutions eist. i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
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"@ (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
@) /rantle* (ollege has decided to DwireD its campus. The frst stage in this e!ort is to install the D3ac+3oneD i.e. to connect all the 3uildings. The ta3le 3elow gi;es the distances 3etween the ;arious 3uildings on campus in hundreds o eet.
Answer: (onnect: 1 " " 6 6 9 0 8 8 9. Total length is 19?? eet. i!: 0 Topic: ,#$#,AL S-A$$#$ T%EE -%&/LE, AA(S/: Anal*tic S+ills -
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=?) i;en a networ+ with the ollowing distances: From $ode 1 1 " " 0 0 0 6 6 8 8 9
To $ode " 6 0 6 6 8 9 8 9
istance 6 1 " 0 9 6 " 8 8 = 6
Ca) etermine which nodes should 3e connected to get the minimum distance 2owing rom $ode 1 through $ode . C3) etermine the minimum distance. Answer: Ca) (onnect: 1 6 6 . Ca) ,inimum distance 9 i!: 0 Topic: S<&%TEST %&'TE -%&/LE, AA(S/: Anal*tic S+ills -
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0? (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
=1) The east to west C(it* 8 to (it* 1) air trac s*stem passing through the '.S. can handle aircrat 2ows with capacities in hundreds o planes per hour as shown. 5hat is the pea+ air trac load in aircrat per hour rom (it* 8 to (it* 1 that this s*stem can handleH -
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Answer: 8?? aircrat per hour. i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
=") A water compan* is anal*7ing the 2ow o water through pipes in an oce 3uilding. The 2ow capacities are gi;en in the ta3le 3elow. Flow is measured in 1?? gallonsBhour. 5hat is the maimal 2ow o water rom node 1 to node 8H
Answer: ?? gallons per hour. i!: 0 Topic: ,A4#,AL FL&5 -%&/LE, AA(S/: Anal*tic S+ills -
=0) escri3e the steps o the shortest route technique. Answer: C1) Find the nearest node to the origin Cplant). -ut the distance in a 3o 3* the node. C") Find the net nearest node to the origin Cplant) and put the distance in a 3o 3* the node. #n some cases se;eral paths will ha;e to 3e chec+ed to fnd the nearest node. C0) %epeat this process until *ou ha;e gone through the entire networ+. The last distance at the ending node will 3e the distance o the shortest route. ou should note that the distance placed in the 3o 3* each node is the shortest route to this node. These distances are used as intermediate results in fnding the net nearest node. i!: 0 Topic: S<&%TEST %&'TE -%&/LE, -
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=6) /rie2* descri3e the minimal spanning technique. Answer: determines the path through a networ+ that connects all the points while minimi7ing the total distance i!: " Topic: #$T%&'(T#&$ -
01 (op*right > "?1" -earson Education #nc. pu3lishing as -rentice
