BM 103 Exersice 11

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    Exercise 11

    1) Solve the ff. Modified Distribution (MODI) Warehouse

    A1:V1+W1= 3, W1= 3

    B1:V1+W2= 5, W2= 5B2:V2+W2= 8, V2= 3

    C2:V2+W3= 4, W3= 1

    C3:V3+W3= 4, V3= 3

    VC

    C1: 3 0 1 = 2

    A2: 4 3 3 = -2

    A3: 3 3 3 = -3

    B3: 8 3 5 = 0

    A3:

    A B C

    1 3 5 3 30

    2 4 8 4 30

    3 3 8 4 25

    20 35 30 8585

    W1=3 W2=5 W3=1

    V1=0 3 5 3 30

    V2=3 4 8 4 30

    V3=3 3 8 4 25

    20 35 30 8585

    - 3 5

    - 8 4

    3 - 4

    - 3 5

    - 8 4

    3 - 4

    20

    10

    255

    25

    20

    10

    25

    5

    25

    10

    20

    25

    5

    25

    20

    30

    5 25

    5

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    Table 2:

    OC

    B1: V1+W2= 5, W2 = 5

    B2: V2+W2= 8, V2 = 3

    C2: V2+W3= 4, W3 = 1

    A3: V3+W1= 3, W1 = 0

    C3: V3+W3= 4, V3 = 3

    VC CC

    A1: 3 0 0 = 3 150 + 40 + 100 + 60 + 20

    C1: 3 0 0 = 3 = 370

    A2: 4 3 0 = 1B3: 8 3 5 = 0

    W1=0 W2=5 W3=1

    V1=0 3 5 3 30

    V2=3 4 8 4 30

    V3=3 3 8 4 25

    20 35 30 8585

    20

    25

    5

    30

    5

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    2)

    OC

    A1: V1+W1 = 30, W1 = 30

    A2: V2+W1 = 30, V2 = 0

    B2: V2+W2 = 50, W2 = 50

    B3: V3+W2 = 60, V3 = 10

    VC

    B1: 30 0 50 = -20

    A3: 40 10 30 = 0

    B1:

    - 30 30

    30 - 50

    Table 2:

    OC

    A1: V1+W1= 30, W1 = 30

    B1: V1+W2= 30, W2 = 30

    A2: V2+W1= 30, V2 = 0

    B3: V3+W2= 60, V3 = 30

    VC

    A B

    1 30 30 25

    2 30 50 15

    3 40 60 30

    30 40 7070

    W1 = 30 W2 = 50

    V1 = 0 30 30 25

    V2= 0 30 50 15

    V3= 10 40 60 30

    30 40 7070

    - 30 30

    30 - 50

    W1 = 30 W2 = 30

    V1 = 0 30 30 25

    V2= 0 30 50 15

    V3= 30 40 60 38

    30 40 7070

    2

    51

    05 3

    0

    2

    5

    1

    053

    0

    2

    5

    51

    0

    1

    5

    1

    5

    1

    0

    1

    5

    1

    0

    1

    5 3

    0

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    B2: 50 0 30 = 20

    A3: 40 30 30 = -20

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    A3:

    Table 3:

    OC

    B1: V1+W2= 30, W2= 30

    A2: V2+W1= 30, V2= 20

    A3: V3+W1= 40,W1= 10

    B3: V3+W2= 60, V3= 30

    VC: CC

    A1: 30 0 10 = 20 B1: 750

    B2: 50 20 30 = 0 A2: 450

    A3: 1200

    B3: 1800

    4200

    - 30 + 30

    + 40 - 60

    - 30 + 30

    + 40 - 60

    W1 = 10 W2 = 30

    V1 = 0 30 30 25

    V2= 20 30 50 15

    V3= 30 40 60 38

    30 40 7070

    15

    30

    10 25

    15

    15

    15

    2

    5

    1

    5 3

    0

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    4)

    OC

    A1: V1+W1 = 30, W1= 30B1: V1+W2 = 30, W2= 30

    B2: V2+W2 = 50, V2= 20

    B3: V3+W2 = 60, V3= 30

    VC

    A2: 25 20 30 = -25

    A3: 30 30 30 = -30

    A3:

    Table 2

    OC

    A1: V1+W1= 30, W1 = 30

    B1: V1+W2= 30, W2 = 30

    B2: V2+W2= 50, V2 = 20

    A3: V3+W1= 30, V3 = 0

    VC

    A2: 25 20 30 = -25

    B3: 60 0 30 = 30

    A B

    1 30 30 35

    2 25 50 19

    3 30 60 16

    30 40 7070

    - 30 + 30

    + 30 - 60

    - 30 + 30

    + 30 - 60

    W1 = 30 W2 = 30

    V1= 0 30 30 35

    V2= 20 25 50 19

    V3= 30 30 60 16

    30 40 7070

    W1 = 30 W2 = 30

    V1= 0 30 30 35

    V2= 20 25 50 19

    V3= 0 30 60 16

    30 40 7070

    3

    01

    9

    5

    1

    6

    3

    05

    1

    6

    1

    4

    2

    1

    1

    6

    3

    01

    9

    5

    1

    6

    1

    41

    9

    2

    1

    1

    6

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    A2:

    30 30

    25 50

    Table 3

    OC

    B1: V1+W2= 30, W2= 30

    A2: V2+W1= 25, W1= 5

    B2: V2+W2= 50, V2= 20

    A3: V3+W1= 30, V3= 25

    VC CC

    A1: 30 0 5 = 25 B1: 1050

    B3: 60 25 30 = 5 A2: 350

    B2: 250

    A3: 480

    2130

    30 30

    25 50

    W1 = 5 W2 = 30

    V1= 0 30 30 35

    V2= 20 25 50 19

    V3= 25 30 60 16

    30 40 7070

    1

    4

    2

    1

    1

    9

    1

    4

    3

    5

    5

    1

    4

    5

    3

    5

    1

    6

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    5) Aling Milling, a fruit trader, sells fruits to shoppers in Manila, Quezon City, and

    Caloocan City, the monthly demand is 5000 kilos in Metro Manila, 3000 kilos in Quezon

    City, and 2000 kilos in Caloocan City. The fruits are shipped from Laguna, Batangas, and

    Mindoro. The monthly supply offered in Laguna is 4000 kilos, in Batangas, is 3500 kilos,

    and 2500 kilos in Mindoro.

    The shipping cost per kilos is shown below

    To Manila Caloocan City Quezon City

    From

    LAGUNA 5 55 60

    BATANGAS 64 66 60

    MINDORO 74 75 80

    What is the lowest transportation cost?

    OCA1:V1+W1 = 5, W1 = 5

    A2:V2+W1 = 64, V2 = 59

    B2:V2+W2 = 66, W2 = 7

    C2:V2+W3 = 60, W3 = 1

    C3:V3+W3 = 80, V3 = 79

    VC

    B1: 55 7 0 = 48 A3: 74 79 5 = -10

    C1: 60 0 1 = 59 B3: 75 79 7 = -11

    B3:

    66 60

    75 80

    Manila, 5 Caloocan, 7 Quezon, 1Laguna, 0 5 55 60 4000

    Batangas, 59 64 66 60 3500

    Mindoro, 79 74 75 80 2500

    5000 2000 300010000

    10000

    66 60

    75 80

    400

    0

    100

    0

    200

    0500

    250

    0

    200

    0500

    250

    0

    200

    0

    250

    0

    500

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    Table 2:

    OC

    A1: V1+W1=5,W1=5

    A2: V2+W1=64,V2=59

    C2: V2+W3=60,W3=1

    B3: V3+W2=75, W2=-4C3: V3+W3=80, V3=79

    VC

    B1: 55 + 4 0 = 59 B2: 66 + 4 - 59 = 11

    C1: 60 0 1 = 59 A3: 74 5 79 = -10

    A3:

    Table 3:

    CC

    A1: 20000

    A2: 32000

    C2: 180000

    A3: 37000

    B3: 150000

    419000

    OC

    A1: V1+W1=5, W1=5 A3: V3+W1=74, V3= 69

    B2:V2+W1=64, V2=59 B3: V3+W2=75, W2= 6

    C2:V2+W3=60, W3=1

    VC

    B1: 55 0 1 = 49 B2: 66 59 6 = 1

    C1: 60 0 1 = 59 C3: 80 69 1 = 10

    Manila 5 Caloocan -4 Quezon 1Laguna 0 5 55 60 4000

    Batangas 59 64 66 60

    3500Mindoro 79 74 75 80 2500

    5000 2000 3000 1000010000

    64 60

    74 80

    64 60

    74 80

    Manila 5 Caloocan 6 Quezon 1Laguna 0 5 55 60 4000

    Batangas 59 64 66 60 3500

    Mindoro 69 74 75 80 2500

    5000 2000 3000 1000010000

    400

    0

    100

    0

    200

    0

    250

    0

    500

    100

    0

    250

    0

    500

    500300

    0

    500

    400

    0

    500

    200

    0

    300

    0

    500

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    6) Using the MODI, find the minimum cost by filling up the following Tables:

    Table I

    W1 = 3 W2 = 1

    A B

    V1= 0 1 3 1 10

    V2= 2 2 5 3 12

    V3= 3 3 2 4 8

    17 13 30

    CC OC VC

    A1: 30 A1: V1+W1 = 3 B1: 1 1 0 = 0

    A2: 35 A2: V2+W1 = 5 A3: 2 3 3 = -4

    B2: 15 B2: V2+W2 = 3

    B3: 32 B3: V3+W2 = 4

    Table II

    W1 = 3 W2 = 5

    A B

    V1= 0 1 3 1 10

    V2= -2 2 5 3 12

    V3= -1 3 2 4 8

    17 13 30

    CC OC VC

    A1: 30 A1: V1+W1 = 3 B1: 1 5 0 = -5

    B2: 36 B2: V2+W2 = 3 A2: 5 + 2 3 = 4

    A3: 14 A3: V3+W1 = 2

    B3: 4 B3: V3+W2 = 4

    10

    75

    8

    10

    7

    12

    1

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    Table III

    W1 = 3 W2 = 1

    A B

    V1= 0 1 3 1 10

    V2= 2 2 5 3 12

    V3= -1 3 2 4 8

    17 13 30

    CC OC VC

    A1: 27 A1: V1+W1 = 3 A2: 5 2 3 = 0

    B1: 1 B1: V1+W2 = 1 B3: 4 + 1 1 = 3

    B2: 36 B2: V2+W2 = 3

    A3: 16 A3: V3+W1 = 2

    80

    9

    8

    12

    1