M
ASSACHUSETTS
I
NSTITUTE OF
T
ECHNOLOGY
15.053 – Optimization Methods in Management Science (Spring 2007)
Recitation 7, April 12
th
and April 13
th
, 2007
Problem 1: FordFulkerson Algorithm
Consider the following Maximum Flow network.
s
1
3
4
2
t
7
5
3
4
6
3
2
8
And consider the following residual network resulting from two iterations of the Ford
Fulkerson algorithm.
s
1
3
4
2
t
2
3
4
4
1
5
5
2
2
2
8
Part A:
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View Full DocumentPerform the final two iterations of the FordFulkerson algorithm to determine the
maximum flow.
Part B:
Determine the corresponding minimum cut based on the final residual network.
Problem 2: Minimum Cost Network Flow Formulation
Each year, Data Corporal produces as many as 400 computers in Boston and 300
computers in Raleigh.
Los Angeles customers must receive 400 computers, and 300
computers must be supplied to Austin computers.
Producing a computer costs $800 in
Boston and $900 in Raleigh.
Computers are transported by plane and may be sent
through Chicago.
The costs of sending a computer between pairs of cities are shown in
the following table.
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 Spring '07
 JamesOrli
 Management, Shortest path problem, Flow network, Maximum flow problem, Maxflow mincut theorem, Minimum cost flow problem, Raleigh

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