HW11_Sol-1

# HW11_Sol-1 - the new machine for three more years(until...

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E160 Operations Research I Spring 2009 Homework #11 Solution Chapter 8 Section 8.2 4. Step 0: i=0, P={1}, l(1)=0 Iteration 1: i=2, l(2)=2, b(2)=1, P={1, 2} Iteration 2: i=3, l(3)=0, b(3)=2, P={1, 2, 3} Iteration 3: i=4, l(4)=1, b(4)=3, P={1, 2, 3, 4} Section 8.4 4. (a) (b) The critical path is 0->A->C->G->12. Question 3

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Let T denote the minimum spanning tree of the graph G. Let N1:={ k| k and i are connected in T\{(i,j)}, N2:={ k| k and j are connected in T\{(i,j)} Since G’ is connected. There must be an edge having one end node in N1 and the other end node in N2. Choose the edge (k*,l*) in G’ such that w(k*,l*)=min{w(k,l)≤w(k,l)| k N1, l N2} and k* N1, l* N2. Section 8.2 7. Let c ij = cost incurred if a machine is purchased at beginning of year i and is kept until beginning of year j. Then we may formulate the problem of minimizing total cost incurred over 5 years as a transshipment problem: We should first keep the machine for two years and then trade it in. Then we should keep
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Unformatted text preview: the new machine for three more years (until problem is over). 8. Let c ij = cost of storing books >i inches and ≤ j inches on a single shelf.c 04 = 2300 + 200(.5)(4)(5) = \$4300 c 08 = 2300 + 300(.5)(8)(5) = \$8300 c 0,12 = 2300 + 380(.5)(12)(5) = \$13,700 c 4,8 = 2300 + 100(.5)(5)(8) = \$4300 c 4,12 = 2300 + .5(180)(5)(12) = \$7700 c 8,12 = 2300 + .5(5)(12)(80) = \$4700 It is easily found that the shortest path from 0 to 12 is 0- 4-12 (cost of \$12,000). Thus a 4" shelf should be built for 4" books, and a 12" shelf is built for 8" and 12" books. Section 8.4 5. Activity A B C D E F G Earliest Starting time 5 13 13 13 17 17 Latest Starting time 5 13 19 13 17 23 Critical path: Start->A->B->C->G->End Start->A->B->E->F->G->End 6. Activity A B C D E F Earliest 2 6 6 9 6 Latest 2 6 7 9 13 The critical path is Start->A->B->C->E->End. 7. Activity A B C D E F G Earliest 3 3 17 25 29 37 Latest 23 3 17 25 29 37 The critical path is Start->A->C->D->E->F->G->End....
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## This note was uploaded on 09/06/2009 for the course IEOR 160 taught by Professor Hochbaum during the Spring '07 term at Berkeley.

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HW11_Sol-1 - the new machine for three more years(until...

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