Group A

.

Solve the following unbalanced transportation problem (symbols have their usual meanings)

Cost information (in Rs.)

Destination

Origin

D1 D2 D3 Supply

O1 19 18 25 100

O2 16 20 15 130

O3 18 23 21 120

Requirement 180 60 110

1. Jensen, Solberg, and Zorn investigated the relationship of insider ownership, debt, and dividend policies in companies. One of their findings was that firms with high insider ownership choose lower levels of both debt and dividends. Shown here is a sample of data of these three variables for 10 different industries. Use the data to develop the equation of the regression model to predict insider ownership by debt ratio and dividend payout.

Industry Insider Ownership

Debt Ratio Dividend Payout

Mining 9 14 10

Food and beverage 18 20 14

Furniture 11 18 12

Publishing 28 18 11

Glass and cement 15 24 12

Motor vehicle 15 15 12

Department store 18 20 7

Restaurant 13 23 11

Transport 18 40 4

Hospitals 10 30 9

(a) Determine the best fit equation for these data. Estimate insider ownership if the debt ratio is 30 and dividend payout is 8

(b) Interpret the regression coefficients.(c) Compute the coefficient of multiple determinations and interpret it.

2. A research firm is planning a questionnaire survey on ‘sexual harassment to office lady’. The following are the activities to be carried out for the survey:

Activity Predecessor tm to tp

A –Design of questionnaire

B –Sampling design

C –Testing of questionnaire and refinements

D –Recruiting for interviewers

E –Orientation to interviewers

F –Allocation of areas to interviewers

G –Conducting interviews

H –Evaluation of results

None

None

A

B

D, A

B

C, E, F

G

5

12

5

3

2

5

14

20

4

8

4

1

2

4

10

18

6

16

12

5

2

6

18

34

a) What are the expected task durations and the variances of task durations?

b) Draw a network for the project and find the critical path. What is the expected duration of the project?

c) What is the probability that the project will not exceed 60 days?

Group B

3. Mega Commercial Bank has four new tellers with varying skills who are to be assigned to the Head office or one of the Branches. The criterion for assigning tellers to locations is minimal customer waiting time. Customers waiting time (in seconds) is shown in the table below for each of four locations and teller skills. Make teller assignments, using the

assignment algorithm that will minimize overall waiting time. What is the total waiting time index for the optimal assignment?

Teller Skill

Location A B C D

Head Office 40 50 75 35

Putali Sadak Branch 60 40 70 70

Baneshor Branch 100 120 90 70

Balaju Branch 60 30 70 90

4. The small manufacturer employs 5 skilled men and 10 semi-skilled men for making a product in two qualities: a deluxe model and an ordinary model. The production of a deluxe model requires 2-hour work by a skilled man and 2-hour work by a semi-skilled man. According to worker union’s rules, no man can work more than 8 hours per day. The profit of the deluxe model is Rs. 1000 per unit and that of the ordinary model is Rs. 800 per unit. Formulate a linear programming model for this manufacturing situation. Use graphical method to determine the production volume of each model such that the total profit is maximized.

6. Following are time-series data for eight different periods. Compute forecast value for the time period 9 using exponential smoothing method with value of alpha, α = .1. Compute the errors for forecast. Value of the first time period can take as forecast for the second period to use your model.

Time Period Value Time Period Value 1 211 5 2422 228 6 2273 236 7 2174 241 6 203

7. Mrs.Sujaan, supervisor of the Circle O discount chain, would like to examine relationship annual demands for widgets. Demand for widgets is affected by number of factors. She has some feeling that disposable income effective demand for the product She collects data for 6customers given below:

Demand 40 45 50 55 60 70

Income (‘000’) 4 5 6 7 8 9

a) Calculate the degree of relationship and interpret it.

b) Test the significance of your result at 0.05 level of significance.

8. The Kathmandu Builder is interested in seeing whether his apartment rents are typical. Thus, he has taken a random sample of 5 rents and apartment sizes of similar apartment complexes. The data are as follows:

Assuming linear relationship develop equation that describe best relationship for this data. Also estimate likely rent when number of bed rooms in an apartment is 6.

9. Write short notes on any two

a. Tracking signal in forecasting.b. CPM & PERT in network analysis. c. Simple regression.

Apartment 1 2 3 4 5

No. of bedroom 2 1 3 2 2

Rent (in ‘00000’) 33 19 45 31 21