Discrete Mathematics with Graph Theory (3rd Edition) 325

# Discrete Mathematics with Graph Theory (3rd Edition) 325 -...

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Chapter 11 19. A critical path takes 25 days, along A, H, F, C, G, D, E, as shown. The slacks in A( -,0) B, I, and J are 4,1, and 1, respectively. 20. The directed network for this type II scheduling problem is shown. S A 2 323 B(A,3) 5 C(F,12) 3 D(G,18) E(D,25) H(A,6) 8 I(H,14) 2 J(G,23) E D J 0 '\$-_+_--0 T (a) Modifying Dijskstra's algorithm as in the text, we obtain the labels A(S, 2), D(A, 3), B(A,4), C(A, 5), E(B,5), F(B, 6), G(C,8), H(F, 10), I(G, 11), J(I, 14), T(J,14). It takes fourteen days to build a glynskz. The only critical path is SACGI JT. (b) Since C is on the critical path, its slack is O. The slack in
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Unformatted text preview: D is 2, the same as E. 21. (a) Since the time for a given task is independent on which other tasks have already been completed, and since some tasks may occur simultaneously, this is a type II scheduling problem. (b) S(-,O) 10 B (S,1O) W(B,18) CVS(B,12) 1 o The shortest time is the length of the longest path from S to T. This is 23 units of time. (SF, 23) T(A,23) S(CVS,14) (c) The critical path is B, R, DR, SF, A. The slack in cooking the wings is 4. The slack in chopping the vegetables for the salad and making the salad is 8 in each case. The slack in chopping the vegetables for the stirfry is 3....
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