Solve the following questions.

1. The following Table below gives the activities in construction project and time duration.

Project Schedule with Time Duration

Activity	Preceding Activity	Normal Time (Days)
1-2	–	20
1-3	–	25
2-3	1-2	10
2-4	1-2	12
3-4	1-3, 2-3	5
4-5	2-4, 3-4	10

a) Draw the activity network of the project.

2. Perform a Forward and backward pass of the network diagram given below and also find which activity has the early finish as that of late finish.

3. Job Saint has laid out the major steps and eight activities to complete the wing assembly for an experimental air craft. These activities have been labeled A to H in the following table, which also shows their estimated completion time (in weeks) and immediate predecessors.

Activity Immediate Predecessorsamb

A———123

B——–234

CA456

DB8910

EC258

FC, G456

GD, E123

(a)Determine expected time and the variance for all the activities.

(b)Determine the earliest start and finish, latest start and finish time and also find slack time for each activities and the project completion time.

4. A dentist schedules all his patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending on the type of dental work to be done. The following summary shows the various categories of work, their probabilities and the time actually needed to complete the work:

Category	Time Required	No. of Patients
Filling	45 minutes	40
Crown	60 minutes	15
Cleaning	15 minutes	15
Extracting	45 minutes	10
Check Up	15 minutes	20

Simulate the dentist’s clinic for four hours and find out the average waiting time as well as the idleness of the doctor.

Assume all the patients show up at the clinic at exactly their scheduled arrival time starting at 8:00am. Use the following random numbers, 40, 82, 11, 34, 25, 66, 17, 70.

5. The number of cars arriving at a self-service gasoline station during the last 50 hours of operation are as follows:

Number of cars arrivingFrequency

610

714

818

98

(a)Set up a probability and cumulative probability distribution for the variable of car arrivals.

(b)Estimate random number intervals for the variables.

(c)The following random numbers have been generated: 99, 98, 26, 09, 49, 52, 33, 89, 21, and 37. Simulate 10 hours of arrivals at this gas station. What is the average number of arrivals during this period?

6. A car rental agency has collected the following data on the demand for five-seater vehicles over the past 50 days.

Daily Demand	4	5	6	7	8
No. of Days	4	10	16	14	6

The agency has only 6 cars at present.

i) Use the following 5 random numbers to generate 5 days of demand for the rental agency:

Random No.s: 15, 48, 71, 56, 90

ii) What is the average number of cars rented per day for the 5 days?

iii) How many rentals will be lost over the 5 days?