Q5 Mudd, Waters & Soeurs constructs major drainage systems for parks, buildings,
ID: 3174352 • Letter: Q
Question
Q5 Mudd, Waters & Soeurs constructs major drainage systems for parks, buildings, and roads. They have six jobs on their worklist see table). A What is the total number of different sequences to process the jobs? B How many ossible secuences would be ossible if there were 20 jobs on he to do list? CIf a computer could test a billion sequences per second, how long would it take the computer to test all possible sequences? Job Characteristics Estimated Processing Time Job (weeks) Due Date Time to Due Date 1-Aug One month (1. 3 weeks) 1-Aug One month 4. 3 weeks) 1-Nov Four Month (17.2 weeks) 1-Oct Three Months (12. 9 weeks) E 10 1-Nov Four Months (17. 2 weeks) 6 1-Dec Five Months (21. 5 weeks)Explanation / Answer
a) Total number of different sequences to process the jobs.
There are 6 different jobs which should be processed one at a time.
In the first position there are 6 possibilities and after that 5 and after that 4 and so on till the last job left out.
i.e. 6*5*4*3*2*1 = 6! ways = 720 different sequences
b) Hence by the above formula if there are 20 jobs then there are 20! ways = 2432902008,176,640,000 ways
c) 1 billion in 1 second. 3600 billion in 1 hour.
20! sequences in 20!/(3600*24*365) yrs i.e. 77 yrs
d) Assuming that the due date can be breached, we can sort the jobs by processing time to get the sequence. Because if the small jobs are completed first then the waiting time for the rest of the jobs will be reduced. Example - if we take the 70 day job first, for the 5 jobs the waiting time is 350 days where as if we take the 7 day job first the waiting time is only 35 days.
As the second case if we give importance to the due date as well, then we will sort it by the remaining time and then sort by processing time. It will lead to 3 jobs completed in time and will be left with 3 jobs overshooting the deadline. However the overshot time will be minimised if we sort the jobs by processing time as second level. We get the following table as a result of this.
Jobs Due date from 1 july Processing time Waiting time C 120 7 0 A 30 14 7 0 B 30 21 7 14 0 D 90 35 7 14 21 0 F 150 42 7 14 21 35 0 E 120 70 7 14 21 35 42 0 Total 189 35 56 63 70 42 0 455Related Questions
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