Operations Research

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Operations Research

Answered Same Day Dec 26, 2021

Solution

David answered on Dec 26 2021

102 Votes

A.
Solution:
TOTAL no. of supply constraints : 3
TOTAL no. of demand constraints : 4
Problem Table is

`D_1` `D_2` `D_3` `D_4`

Supply
`S_1` 9 8 6 7

25
`S_2` 100 9 15 8

15
`S_3` 6 12 10 100

10
Demand 5 20 15 10
The rim values for `S_1`=25 and `D_1`=5 are compared.
The smaller of the two i.e. min(25,5) = 5 is assigned to `S_1` `D_1`
This meets the complete demand of `D_1` and leaves 25 - 5 = 20 units with `S_1`
Table-1

`D_1` `D_2` `D_3` `D_4`

Supply
`S_1` 9 (5) 8 6 7

20
`S_2` 100 9 15 8

15
`S_3` 6 12 10 100

10
Demand 0 20 15 10
The rim values for `S_1`=20 and `D_2`=20 are compared.
The smaller of the two i.e. min(20,20) = 20 is assigned to `S_1` `D_2`
This exhausts the capacity of `S_1` and leaves 20 - 20 = 0 units with `D_2`
Table-2

`D_1` `D_2` `D_3` `D_4`

Supply
`S_1` 9 (5) 8 (20) 6 7

0
`S_2` 100 9 15 8

15
`S_3` 6 12 10 100

10
Demand 0 0 15 10

The rim values for `S_2`=15 and `D_2`=0 are compared.
The smaller of the two i.e. min(15,0) = 0 is assigned to `S_2` `D_2`
This meets the complete demand of `D_2` and leaves 15 - 0 = 15 units with `S_2`
Table-3

`D_1` `D_2` `D_3` `D_4`

Supply
`S_1` 9 (5) 8 (20) 6 7

0
`S_2` 100 9 15 8

15
`S_3` 6 12 10 100

10
Demand 0 0 15 10
The rim values for `S_2`=15 and `D_3`=15 are compared.
The smaller of the two i.e. min(15,15) = 15 is assigned to `S_2` `D_3`
This exhausts the capacity of `S_2` and leaves 15 - 15 = 0 units with `D_3`
Table-4

`D_1` `D_2` `D_3` `D_4`

Supply
`S_1` 9 (5) 8 (20) 6 7

0
`S_2` 100 9 15 (15) 8

0
`S_3` 6 12 10 100

10
Demand 0 0 0 10
The rim values for `S_3`=10 and `D_3`=0 are compared.
The smaller of the two i.e. min(10,0) = 0 is assigned to `S_3` `D_3`
This meets the complete demand of `D_3` and leaves 10 - 0 = 10 units with `S_3`
Table-5

`D_1` `D_2` `D_3` `D_4`

Supply
`S_1` 9 (5) 8 (20) 6 7

0
`S_2` 100 9 15 (15) 8

0
`S_3` 6 12 10 100

10
Demand 0 0 0 10
The rim values for `S_3`=10 and `D_4`=10 are compared.
The smaller of the two i.e. min(10,10) = 10 is assigned to `S_3` `D_4`...

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