1)
London | Ottawa | Kinngston | Quebecc | Capacities | |||
Toronto | 6 | 9 | 8 | 13 | 500 | ||
Montreal | 12 | 17 | 6 | 7 | 400 | ||
halifax | 1 | 14 | 13 | 10 | 300 | ||
Requirements | 450 | 350 | 250 | 150 | |||
The objective here is to minimize the transportation cost Z.
Let X be the number of units.
i = 1 toronto, 2 montreal, 3 halifax
j= 1 london, 2 ottawa, 3 kingston ,4 quebecc
1 1 represent units transferred from toronto to london
1 2 represents units from toronto to ottawa
1 3 represent units from toronto to kingston likewise 1 4 represent units from toronto to quebecc
formulations:
Minimize Z = 6X11 + 9X12 + 8X13+13X14+12X21+17X22+6X23+7X24+1X31+14X32+13X33+10X34
Subject to constraints:
X11+X12+X13+X14 =500
X21+X22+X23+X24=400
X31+X32+X33+X34=300
X11+X21+X31 =450
X12+X22+X32=350
X13+X23+X33=250
X14+X24+X34=150
X110
X120
X130
X140
X210
X220
X230
X240
X310
X320
X330
X340
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