Discrete Mathematics with Graph Theory (3rd Edition) 316

Discrete Mathematics with Graph Theory (3rd Edition) 316 -...

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314 Solutions to Exercises Po(G,12) 4 A(8h,20) 4 R(A,24) 8 ( -, 0) G---I ..... 7 ---4 JiT--_+----,I) T(Pa, 31) o 8h(G,16) 5 H(A,25) 6 Pa(H,31) (b) The slack in Po is still 4. If Po takes nine months, the label on Po would be (G,16) and the label on A could be either (Sh, 20) or (Po, 20). There would then be a second critical path. If Po took more than nine months, the label on A would increase and the total time of the project would increase. There is no slack in Sh and A since these are on the critical path. The slack in Tw is 4. The slack in R is 7. (c) If Po and A are each delayed three months, the project will be delayed three months as well. The label on Po would become (G, 15) and the label on A would become (Sh, 23). Then H would be (A, 28) and Pa, (H, 34). The critical path would be SGShAH PaT as before, but the project would now require 34 months. 9. Looking at the answer to Exercise 7, we see that the label on
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Unformatted text preview: A would become (Sh, 22) while R would acquire the new label (A,29). Vertex Tw would be labeled (A,24). The critical path would now be SGShART requiring 29 months. 10. Have you ever seen a Mobius strip? Take a strip of paper, give it a single twist and glue the ends together. What you get is a strip with just one side! Notice that the original strip was 2-dimensional, but the Mobius strip only exists in three dimensions. A Klein bottle is a similar sort of thing, but unfortunately it exists only in four dimensions so, while there are many pictures of it (there is a Klein bottle web site, www.kleinbottle.com.containingsomemarvelouspictures).itis in fact an imaginary object. It's a bottle without a boundary. You can't tell inside from out! 11. (a) [BB] This type I scheduling problem is described by the following digraph. @ B(A,7) 4 8(-,0) ":;&""""-f> T(M, 12) E(8,2) (b) [BB] The shortest time is 12 units....
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