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Chapt 18

# Chapt 18 - Dynamic Programming 2 a The numbers in the...

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Dynamic Programming 2. a. The numbers in the squares above each node represent the shortest route from that node to node 10. 1 2 3 4 6 5 9 8 7 10 26 19 10 18 21 11 17 6 8 10 8 5 4 6 8 7 7 9 10 5 11 6 10 8 The shortest route is given by the sequence of nodes (1-4-6-9-10). b. The shortest route from node 4 to node 10 is given by (4-6-9-10). c. Route Value Route Value (1-2-5-7-10) 32 (1-3-6-8-10) 34 (1-2-5-8-10) 36 (1-3-6-9-10) 31 (1-2-5-9-10) 28 (1-4-6-8-10) 29 (1-3-5-7-10) 31 (1-4-6-9-10) 26 (1-3-5-8-10) 35 (1-3-5-9-10) 27 See 1 above for an explanation of how the computations are reduced. 3. Use 4 stages; one for each type of cargo. Let the state variable represent the amount of cargo space remaining. a. In hundreds of pounds we have up to 20 units of capacity available. Stage 1 (Cargo Type 1) x 1 0 1 2 * 1 d f 1 ( x 1 ) x 0 0-7 0 - - 0 0 0-7 8-15 0 22 - 1 22 0-7 16-20 0 22 44 2 44 0-4 Stage 2 (Cargo Type 2) x 2 0 1 2 * 2 d f 2 ( x 2 ) x 1

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Chapter 18 0-4 0 - - 0 0 0-4 5-7 0 12 - 1 12 0-2 8-9 22 12 - 0 22 8-9 10-12 22 12
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Chapt 18 - Dynamic Programming 2 a The numbers in the...

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