Engineering Optimization: Theory and Practice, Fourth Edition

Problems 585

Figure 9.25 Altitudes of the airplane in Example 9.4.

To altitude (ft):
From altitude (ft): 0 8,000 16,000 24,000 32,000 40,000

0 — 4000 4800 5520 6160 6720

8,000 800 1600 2680 4000 4720 6080

16,000 320 480 800 2240 3120 4640

24,000 0 160 320 560 1600 3040

32,000 0 0 80 240 480 1600

40,000 0 0 0 0 160 240

9.5 Determine the path (route) corresponding to minimum cost in Problem 9.2 if a person

wants to travel from cityDto cityM.

9.6 Each of thenlathes available in a machine shop can be used to produce two types of

parts. Ifzlathes are used to produce the first part, the expected profit is 3zand ifz

of them are used to produce the second part, the expected profit is 2. 5 z. The lathes are

subject to attrition so that after completing the first part, onlyz/3 out ofzremain available

for further work. Similarly, after completing the second part, only 2z/3 out ofzremain

available for further work. The process is repeated with the remaining lathes for two more

stages. Find the number of lathes to be allocated to each part at each stage to maximize the

total expected profit. Assume that any nonnegative real number of lathes can be assigned

at each stage.

9.7 A minimum-cost pipeline is to be laid between points (towns)AandE. The pipeline is

required to pass through one node out ofB 1 ,B 2 , andB 3 , one out ofC 1 ,C 2 , andC 3 ,

and one out ofD 1 ,D 2 , andD 3 (see Fig. 9.26). The costs associated with the various

segments of the pipeline are given below:

For the segment starting atA For the segment ending atE

A–B 1 10 D 1 – E 9

A–B 2 15 D 2 – E 6

A–B 3 12 D 3 – E 12