Quantitative methods, transportation model

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(See attached file for full problem description)

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A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

Destination Assembly Plant
1 2 3 Supply
Source A 5 9 16 200
Factory B 1 2 6 400
C 2 8 7 200
Demand 120 620 60

What are the supply constraints for the factories?
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Attachments

A logistics.problem.part2.doc

Solution Preview

Hints:
LP for the above model is
Decision variables:
xa1 be the quantity shipped from factory A to assembly plant 1. Similarly we have
xa2, xa3, xb1, xb2, xb3, xc1, xc2, and xc3

Objective function:
Min: 5 xa1+ 9xa2+ 16xa3+1 xb1+2xb2+6xb3+2xc1+8xc2+7xc3
As it is the case of balanced transportation problem, constraints are
Supply availability
xa1+ xa2+xa3=200
xb1+xb2+xb3=400
xc1+xc2+xc3=200

Demand requirements
xa1+ xb1+ …