Order Description

want you answer the 4 questions its about critical path, control limits and trend projection method i will upload PPT slide explaining everything. i will upload the document with the questions.
Problems
1. Idris Group Inc. (IGI) is a construction company that has presence in many progressive emerging economies such as the UAE. Presently, IGI has a multi-million dirham project in Dubai, UAE. As a newly hired Chief project manager (CPO), you have been charged to manage this particular project. To manage this project effectively and efficiently, you are required to construct a project network diagram to show the various activities associated with the project. Upon completing the drawing the network, you mandated your team to estimate the amount of time that they would expect each of the activities to take. Their responses are shown in the following table:

Time Estimates (Days)
Activity Optimistic Most Likely Pessimistic Immediate Predecessors
A 4 7 10 –
B 3 7 10 –
C 4 5 6 A
D 1 3 5 A
E 3 6 9 B, D

a) Develop the project network and determine the critical path. How long will the project take?
b) What is the probability of completing the project in 20 days?
c) What is the probability of completing the project in 16 days?
2) XYZ produces a lot of boxes of Carmel candies and other assorted sweets that are sampled each hour. To set control limits that 95.5% of the sample means, 35 boxes are randomly selected and weighed. The standard deviation of the overall production of boxes is estimated, through analysis of old records, to be 2 ounces. The average mean of all samples taken is 15 ounces. Calculate control limits for an – chart.

3a) ABC Company that have ventured into manufacturing of environmental friendly lightbulbs. The following data on the number of lumens for 40-watt lightbulbs were collected when the process was in control.

Observation
Sample 1 2 3
1 504 512 488 500
2 497 501 507 503
3 481 470 485 492
4 520 505 495 488
5 490 514 508 504

(i) Calculate control limits for an – chart and R-chart. (ii) Since these data were collected, some new employees were hired. A new sample obtained the following readings: 470, 503, 523, and 483. Is this process still in control?

3b) XYZ has five data entry staffs. Each working day their supervisor verifies the accuracy of a random sample of 150 records. A record containing one or more errors is considered defective and must be done over. The results of the last 30 samples are shown in the table. All were checked to ensure none was out of control.

Sample No. of Defective records

Sample No. of Defective records

Sample No. of Defective records

Sample No. of Defective records
1 6 9 5 17 11 24 6
2 4 10 12 18 3 25 12
3 18 11 17 19 5 26 9
4 9 12 4 20 10 27 13
5 10 13 15 21 16 28 5
6 7 14 3 22 11 29 10
7 11 15 10 23 5 30 8
8 8 16 7
Total 270

Based on the historical data, set up a p-chart for 95.5% confidence.
3c) There have been complaints that the sports page of XYZ has lots of typos. As a result, XYZ decided to assembly a team to investigate the complaints. For the last six days, the team painstakingly examined the records. The following is number of typos/page recorded.

Day Number of Typos
Mon. 3
Tues. 2
Wed. 6
Thurs. 4
Fri. 5
Sat. 1

Construct a control chart with 99.7% confidence. Is the process in control?

4) XYZ produces AME air conditioners for Africa and Middle East markets that are suitable for the hot weather environment. And sales of AME air conditioners have grown steadily during the past 5 years. Following is the historical or time series data of AME air conditioners sales.

YEAR SALES

1 45

2 49

3 51

4 56

5 58

6 ?
_______________________

a) Unfortunately, the sales manager did not predict or forecast before the business started year 1’s sales of AME air conditioners. Using smoothing constant of 0.2 and 0.3, develop forecasts for the sales of AME air conditioners. Which smoothing constant would you recommend to the company to use in forecasting its future sale and why?
b) Using the trend projection method and the data above, develop a forecast model for the sales of AME air conditioners. Using the forecast model you developed, determine the projected sales in year 6?

4). XYZ uses and produces 3,000 brackets in-house during the course of a year, and this usage is relatively constant. Idris has determined that setup costs would be AED 30 in machinist time and lost production time, and 50 brackets could be produced in a day once the machine has been set up. Idris estimates that the cost (including labor time and materials) of producing one bracket would be AED 20. The holding cost would be 10% of this cost. There are 250 working days per year.
a) Determine the optimal production quantity.
b) What is the daily demand rate?
c) Determine how long it will take to produce the optimal quantity. Calculate how much inventory is sold during this time.
d) If Idris uses the optimal production quantity, what would be the maximum inventory level?
e) How much production runs would there be each year
f) Given the optimal production run size, what is the total annual inventory cost?
g) If the lead time is one-half day, what is the reorder point (ROP)?