Assignment 1

Instructions: To answer questions, 1, 2 and 3, you can write the answers on a paper, take a photo, and then copy the image of the answer in this word file. Please make sure to specify the answer for each sub-question.

For question 4, type the correct answer in front of each sub-question. Also, please copy an image of the excel file you answer the question.

When all answers are added. You should upload this Word file on Canvas in the submission link of the assignment.

Question 1- The new president of Miskatonic University has decided on building a pool. She sat down with the contractor and together they determined what activities would have to occur, their precedence relationships, and the estimated duration (in weeks). The data are listed below.

Activity	Predecessor	Time
A	--	6
B	A	3
C	A	9
D	A	10
E	B	4
F	B	2
G	C	12
H	D	3
I	F, G	14
J	E, I, H	4

1. What is the latest finish time for Activity D?
2. What is the earliest finish time for Activity G?
3. What is the slack time for Activity B?
4. What is the duration of the project on the critical path?
5. What is the critical path?

Question 2- A PERT analysis of a project determined that the mean duration of the critical care was 100 weeks and the critical path had a standard deviation of 6 weeks. What is the probability the project will be completed within 115 weeks?

Question 3- Ocean Citys Motor Vehicle Department has two offices. The main office handles 70% of the traffic. They have designed the office into various sections: Initial Processing; Registration; Driving Licenses; License Plate Renewal; and Fines. Everyone flows through Initial Processing, as it assigns everyone to the other sections. Saturday is the busiest day in the Motor Vehicle Department, with people arriving at a rate of 25 per hour following an assumed Poisson distribution. Moving through Initial Processing is straightforward, and on average, it only takes 120 seconds per person, following an assumed exponential distribution. (This is a Single Server Single Phase line structure) (Do not use the Excel calculator to solve this question, use the formulas in the slides)

1. What is the capacity utilization of the system?
2. What would be the probability of having no individuals in the system?
3. What would be the average number of individuals waiting in line?
4. What would be the average time (in minutes) an individual spends in the system?

Question 4- A Starbucks shop decides to install an automatic coffee vending machine outside one of its stores to reduce the number of people standing in line inside. The cost of one coffee on the machine is 3.50$. The service time is a constant 3 minutes, and the arrival rate is 15 person per hour with a Poisson distribution.

(You can use the Excel calculator to solve this question)

1. What is the average wait in line?
2. What is the average number of people in line?
3. Starbucks decides to increase the price to 5$ per cup and take 60 seconds off the service time. But this increase in the price reduce the arrival rate to 10 person per hour. Now, what is the average wait time and the average number of people in the line?