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Discrete Mathematics with Graph Theory (3rd Edition) 324

Discrete Mathematics with Graph Theory (3rd Edition) 324 -...

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322 Solutions to Review Exercises 17. In the directed network for this type I schedul- ing problem, we will let 81, 82, 8L, EP and EM denote, respectively, study session 1, study ses- sion 2, sleep, eating pizza and checking e-mail. I':::'- ..... --JI' T 8 E (a) Applying Dijkstra's algorithm (first version), we obtain the labels B(8,2), A(8,3), E(B,3), C(A,4), D(A,4), H(C or D, 5),G(C, 7), K(H,8), F(C, 9), J(F or H, 10), I(F or G, 12), T(J, 13). So George can complete his activities in thirteen hours using any of the following paths: 8 AC F JT, 8ACHJT,8ADHJT. (b) No. One of the pahts, SADHJT, has him doing this. (c) Yes. In this case, George must do another activity after checking his e-mail and before ordering
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Unformatted text preview: the pizza, and none of the paths in (a) satisfy this. From the network, we can see that this means he must begin in the order 8BDH. It is clear then by inspection that the shortest path will be 8BDH JT, requiring fourteen hours. 18. (a) Since the time for various tasks depends on which tasks have already been completed, this is a Type I scheduling problem. F(H,22) (b) ® ®3 1:1 T(P,30) S( -,0) A(S,3) J( ® ®3 3 @ O(N,20) L(A,6) @ (c) The groceries can be purchased, bagged and on the truck in 30 units time, along the route 8ALJ K I PT....
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