The average number of jobs in the work center for the jobs listed in the following table under the FCFS (first come,first served)rule is ______. $$\begin{array} { | c | c | c | }
\hline \text { Job } & \begin{array} { c }
\text { Processing time } \
\text { (in days\} }
\end{array} & \begin{array} { c }
\text { Due date (in days from } \
\text { today's date\} }
\end{array} \
\hline \text { A } & 4 & 9 \
\hline \text { B } & 10 & 18 \
\hline \text { C } & 6 & 6 \
\hline \text { D } & 12 & 19 \
\hline \text { E } & 7 & 17 \
\hline
\end{array}$$
A)3.5
B)2.1
C)3.23
D)2.79

Question

The average number of jobs in the work center for the jobs listed in the following table under the FCFS (first come,first served)rule is ______. $$\begin{array} { | c | c | c | } 
\hline \text { Job } & \begin{array} { c } 
\text { Processing time } \
\text { (in days\} }
\end{array} & \begin{array} { c } 
\text { Due date (in days from } \
\text { today's date\} }
\end{array} \
\hline \text { A } & 4 & 9 \
\hline \text { B } & 10 & 18 \
\hline \text { C } & 6 & 6 \
\hline \text { D } & 12 & 19 \
\hline \text { E } & 7 & 17 \
\hline
\end{array}$$
A)3.5
B)2.1
C)3.23
D)2.79

Quizplus · Accepted Answer

To calculate the average number of jobs in the work center under the FCFS rule, we need to determine the total time each job spends in the system and then find the average. The total time in the system for each job is the sum of its processing time and the waiting time before it starts processing. Under FCFS, jobs are processed in the order they arrive, so we can calculate the waiting time based on the processing times of the jobs before each job.1. Job A starts immediately, so its total time in the system is its processing time: 4 days.2. Job B starts after A finishes, so its total time in the system is its processing time plus A's processing time: 10 + 4 = 14 days.3. Job C starts after B, so its total time is its processing time plus A's and B's processing times: 6 + 4 + 10 = 20 days.4. Job D starts after C, so its total time is its processing time plus the processing times of A, B, and C: 12 + 4 + 10 + 6 = 32 days.5. Job E starts after D, so its total time is its processing time plus the processing times of A, B, C, and D: 7 + 4 + 10 + 6 + 12 = 39 days.The total time all jobs spend in the system is 4 + 14 + 20 + 32 + 39 = 109 days.The average number of jobs in the work center is the total time divided by the total processing time for all jobs: 109 / (4 + 10 + 6 + 12 + 7) = 109 / 39 = 2.79.Therefore, the correct answer is 2.79, which corresponds to choice D.

The Average Number of Jobs in the Work Center for the Jobs