rec7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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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: Ford-Fulkerson 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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Perform the final two iterations of the Ford-Fulkerson 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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rec7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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