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NYIT Manhattan Campus Qant 300 BirasnavMathuraj Midterm questions + answer...

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Camelia Antoci 1264345 Individual Assignment Midterm Total points: 40 (Answer any 4 Questions) 1: The estimated times (in weeks) and immediate predecessors for the activities in a project at Howard Umrah’s retinal scanning company are given in the following table. Assume that the activity times are independent. Activity

Immediate Predecesso r

Optimistic time

Most likely time

Pessimistic time

A

-

9

10

11

B

-

4

10

16

C

A

9

10

11

D

B

5

8

11

a) Calculate expected time and variance of each activity. b) What is the expected completion time of the critical path?

(4 points) (3 points)

c) Assume that the project completion time follows normal distribution, what is the probability of completing this project within 21 weeks?

(3 points)

Answers 10 weeks (A)

10 weeks(C)

a)

10 weeks (B)

Project End

8 weeks(D)

b) The expected completion time of the critical path which is AC is 20 weeks.

2. Bill Fennema, president of Fennema Construction, has developed the tasks, durations, and predecessor relationships in the following table for building new motels. Draw the AON network and answer the following questions: Activity

Immediate

Normal time

predecessors A

-

8

B

A

8

C

A

12

D

A

6

E

B

2

F

E, C

8

G

E, C

3

H

F

2

I

F

6

2

J

D, G, H

6

K

I, J

2

1. What is the expected total completion time? 2. What is the critical path? Solution:

3. Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the chip during the past 12 months were as follows: Month

Price per chip

Month

Price per chip

Jan

$1.80

Jul

1.8

Feb

1.67

Aug

1.83

Mar

1.7

Sep

1.7

Apr

1.85

Oct

1.65

May

1.9

Nov

1.7

Jun

1.87

Dec

1.75

a) Use a Naïve approach forecast on all the data starting from February

(3 points)

b) Use a 3-month moving average forecast on all the data starting from April (3 points) c) Draw a graph that should depict actual prices and Naïve approach and 3-month moving average forecast. Which is the best moving average forecast based on mean squared error?

(3 + 1

points) Solution: Months

Actual

Naive

3 period moving average

3

Jan

$1.80

-

Feb

1.67

1.80

Mar

1.7

1.67

Apr

1.85

1.7

1.723

May

1.9

1.85

1.74

Jun

1.87

1.9

1.81

Jul

1.8

1.87

1.873

Aug

1.83

1.8

1.85

Sep

1.7

1.83

1.83

Oct

1.65

1.7

1.77

Nov

1.7

1.65

1.72

Dec

1.75

1.7

1.68

Based on MSE, three period moving average is the best forecasting method as it gives the lowest MSE value.

4. Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: 4

Hour

x

Hour

x

1

3.25”

7

3.05

2

2.10

8

2.65

3

3.22

9

3.02

4

3.39

10

2.85

5

2.07

11

2.83

6

2.86

12

2.97

Develop appropriate chart and determine whether there is any cause for concern in the cutting process. Assume the population standard deviation is 1” and assume Z = 3. (10 points) Solution: The b- bar chart is used to calculate the values of the question. Upper control limit (UCL): = x + Z(sigmax Lower control limit (LCL): = x - Z(sigmax Average of sample means = (3.25 + 2.10 + 3.22 + 3.39 +2.07 +2.86 + 3.05 + 2.65 + 3.02 + 2.85 + 2.83 + 2.97) / 12 Average of sample means = 2.5725 With z = 3, n = 12 observations per sample, and (std = 1, we find UCL = 3.438 LCL = 1.706 In this the UCL is 3.438 and LCL is 1.706 in the figure below.

5

No, there is no cause of concern as the values are within the range of the Upper control limit and lower control limit and the process is going normal.

5. Bob Richards, the production manager of Zychol Chemicals, in Houston, Texas, is preparing his quarterly report, which is to include a productivity analysis for his department. One of the inputs is production data prepared by Sharon Walford, his operations analyst. The report, which she gave him this morning, showed the following:

Production (units) Raw material used (barrels of petroleum byproducts) Labor hours Capital cost applied to the department ($)

2008

2009

4,500

6,000

700

900

22,000

28,000

$375,000

$620,000

Bob knew that his labor cost per hour had increased from an average of $13 per hour to an average of $14 per hour, primarily due to a move by management to become more competitive with a new company that had just opened a plant in the area. He also knew that his average cost per barrel of raw material had increased from $320 to $360. He was concerned about the accounting procedures that increased his capital cost from $375,000 to $620,000, but earlier discussions with his boss suggested that there was nothing that could be done about that allocation. Bob wondered if his productivity had increased at all. He called Sharon into the office and conveyed the above information to her and asked her to prepare this part of the report.

6

Prepare the productivity part of the report for Mr. Richards. He probably expects some analysis of productivity inputs for all factors, as well as a multifactor analysis for both years with the change in productivity (up or down) and the amount noted. [10 points] Productivity Report 2009

6,000

1,500

900 28,000

200 6,000

28.57% 27.27%

700 22,000

$ 620,000

$ 245,000

65.33%

$ 375,000

0.15 $ 360 4.67 $ 14 103.33 100,000 106,000

(0.01) $ 40 (0.22) $1 20.00

-3.57% 12.50% -4.55% 7.69% 24.00%

0.16 $ 320 4.89 $ 13 83.33

Increase Production in units Raw material used in barrels of petroleum by-products Labour hours Capital cost applied to the department ($) Productivity Raw Material (Qty) per unit Raw Material cost per unit Productivity Labour Hours per unit Labour cost per unit Capital cost per unit Total Increase in Material costs Total Increase in labour hours Total capital cost increase should be Excess capital used

2,008 Percentage Increase or (Decrease) 33.33%

4,500

206,000 39,000

Analysis of the report: The consumption of raw materials and labor hours has been increased from the previous year by nearly 28 and 27 percent respectively resulted in the more production of the units in company which has been increased by more than 33 percent. There is also increase in the total capital cost which is increased by 206000. There is also excess capital used which might be due to the reduced credit time allowed by the suppliers.

7...