1. Activity Immediate Predecessor A B D E Activity Time (Days) 5 10 6 7 8 A B, C (a) Draw the Precedence Diagram for the above project complete with ES, EF, LS, and LF. (b) Compute the Critical Path and calculate the Project Completion Time. 2. Pessimistic Expected Variance Time Time (Days) Activity Immediate Optimistic Most Predecessor Time Likely (Days) Time (Days) A 5 7 B A 2 5 B 6 7 D B 4 6 9 14 8 8 (a) Calculate Expected Time and Variance for the four activities and complete the table above. (b) Draw the Precedence Diagram for the above project complete with ES, EF, LS, and LF. (c) Compute the Critical Path and calculate the Project Completion Time. (d) What is the probability that the project will be completed by 22 days? 3. Activity Immediate Predecessor Normal Cost (S) A B D E Normal Time (Days) 8 8 12 6 8 Crash Crash Time Cost (S) (Days) 6 8,000 8 4,000 10 7,000 6 3,000 6 8,000 5,000 4,000 6,000 3,000 7,000 A B B D (a) Draw the Precedence Diagram for the above project, complete with ES, EF, LS, and LF. (b) What is the Critical Path? (c) What is the Project Completion Time under normal schedule? (d) If the total project time has to be crashed by TWO days, which activity will you choose? 4. In a department store, customers arrive at the rate of 30 per hour and the average service time is four minutes. The arrivals are described by Poisson distribution and the service times are exponentially distributed. The store is open 10 hours a day. They have employed three sales clerks. (a) Find (i) the average number of customers in the queue, and (ii) the average time a customer spends waiting in the queue. (b) Waiting cost is $100 per hour and service cost per sales clerk is $10 per hour. Using the values computed in 4 (a) earlier calculate the total of the daily waiting cost and the service cost each day if three sales clerks are used. What is the total daily cost