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Discrete Mathematics with Graph Theory (3rd Edition) 318

Discrete Mathematics with Graph Theory (3rd Edition) 318 -...

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316 14. (a) [BB] Since this is clearly a one-man project (!), it is of type 1. The appro- priate directed network is shown. (b) Carrying out Dijkstra's algorithm (first version) gives the graph shown. There are two critical paths: SBDM and SDMB, each of length 48 minutes. Thus, John can either shower, eat breakfast, dress and do his math assign- ment, or shower, dress, finish his as- signment and eat breakfast. 15. (a) The appropriate directed net- work and the digraph ob- tained by using Dijkstra's al- gorithm are shown. (b) The critical path is S M B D of length 45 minutes corre-
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Unformatted text preview: sponds to showering, finish-ing math assignment, eating breakfast and dressing. Note that there were choices avail-able in the labeling of ver-tices Y and Z. Since Y is the only one of these on the critical path, we conclude that the only other critical path is MSBD. St St(-,O) w v Solutions to Exercises v Y Y(W,39) 9 P 'ls.-=:::. .---e---+-+--~T R P(W,36) T T(X,48) or (Y,48) 0<:::::----'1. ....--=---o_\$) )",. ....:=+----er-t-~-__f) T(R,45) V(St,18) R(Y,36) 16. This is a type I scheduling problem. We draw a digraph whose vertices represent stages in the process...
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