1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

End Semester Examinations –  April 2013

m.com – ii semester

Operations Research for Business Decisions

Duration: 3 Hrs                                                                                                Max. Marks: 100

SECTION – A

1. I) Answer any SEVEN Each carries FIVE  marks.                                                      (7 x 5 = 35)
2. The Handy- Dandy company wishes to schedule the production of a kitchen appliance that requires two resources- labour and material. The company is considering three different models and its production engineering department has furnished the following data. Supply of raw material is restricted to 200 Kgs. Per day. The daily availability of labour is 150 hrs. formulate a linear programming model to determine the daily production rate of the various models in order to maximize the total profit. Formulate the problem and write the dual.

	Models
	A	B	C
Labour ( hrs per unit)	7	3	6
Material ( kgs. Per unit)	4	4	5
Profit ( Rupees per unit)	40	20	30

 

2. Use graphical method to solve the following Linear Programming Problem.

Minimize Z= 40x + 36y

Subject to constraints

X<=8

Y<=10

5X + 3Y >=45

Where x, y  >=0

3. Define Operation Research. Explain the main phases of an OR study.
4. Which are the special variables used in Simplex and Big M Method. Explain how and why they are used? What do they indicate?
5. Explain the terms: i) feasible solution     ii) optimal solution     iii) unrestricted variables
6. iv) Unbounded solution v) redundancy constraint
7. Using least cost method find an initial solution to the transportation problem to maximize profit.

To-> From	D1	D2	D3	D4	Availability
S1	40	25	22	33	100
S2	44	35	30	30	30
S3	38	38	28	30	70
Requirement	40	20	60	30

 

7. In an Assignment problem explain the following special cases
8. i) unbalance                ii) maximization            iii) Prohibited assignment
9. iv) multiple optimal solution    v) travelling salesman problem
10. Give some applications of queuing theory and explain the terms
11. i) queue         ii) traffic intensity         iii) service channel          iv) queue discipline      v) balking
12. A confectioner sells confectionery items. Past data of demand per week in hundred kilograms with frequency is given below:

Demand/week	0	5	10	15	20	25
Frequency	2	11	8	21	5	3

Using the following sequence of random numbers, simulate the demand for the next 10 weeks. Also find the average demand per week.

Random Numbers: 35, 52, 90, 13, 23, 73, 34, 57, 37, 83

10. Define dynamic programming problem. List and explain the terminologies of dynamic programming problem.

SECTION –  B

III)   Answer any THREE questions.  Each carries FIFTEEN marks.                                                   (3×15 = 45)

11. Solve the following LPP using Simplex Method

Maximize Z= 3x + 2y

Subject to,

-x +2y <= 4

3x + 2y <=14

X – y <=3

Where x, y >= 0

12. Stronghold construction Company is interested in taking loans from banks for some of its projects P, Q, R, S, T. the rates of interest and the lending capacity differ from bank to bank. All these projects are to be completed. The relevant details are provided in the following table. Assuming the role of a consultant, advice this company as to how it should take the loans so that the total interest payable will be the least. Are there alternate optimal solution? If so indicate one such solution.

Bank	Interest rates in % for projects					Maximum Credits ( in thousands)
	P	Q	R	S	T
Pvt.  Bank	20	18	18	17	17	Any amount
Nationalised Bank	16	16	16	15	16	400
Co-operative Bank	15	15	15	13	14	250
Amount required ( in thousands)	200	150	200	125	75

 

13. A company has four sales representatives who are assigned to four different sales territories. The monthly sales increase estimated for each sales representative for different sales territories ( in lakh rupees) are shown in the following table. Suggest an optimal assignment and the total maximum sales increase per month. If for certain reasons sales representative ‘B’  cannot be assigned to sales territory III, will the optimal assignment schedule be different? If so find that schedule and effect on total sales.

Sales Territories-> Sales Representatives	I	II	III	IV
A	200	150	170	220
B	160	120	150	140
C	190	195	190	200
D	180	175	160	190

 

 

 

 

 

 

14. The extension counter of the Citizen’s bank in the premises of a state university enrolls all new customers (students) in savings bank accounts. In the month of August , as the classes begin a lot of new accounts have to be opened for new students enrolled. The bank manager estimates that the arrival rate during this period will be poisson distributed with an average of 3 customers per hour. The service is exponentially distributed with an average of 15 minutes per customer to set up a new account. The bank manager wants to determine the operating characteristics for this system to know whether the current strength of one server is sufficient to handle the increased traffic. Analyse the problem by determining all factors connected with the queueing system.
15. Solve the following capital budgeting problem using dynamic programming.

An organization is planning to diversify its business with a maximum outlay of 5 crores. It has identified three different locations to install plants. The organization can invest in one or more of these plants subject to the availability of these funds. The different possible alternatives and their investment (in crores of rupees) and present worth of returns during useful life (in crores of rupees) of each of these plants are summarized in the table. Find the optimal allocation of the capital to different plants which will maximize the corresponding sum of the present worth of returns.

Alternatives	Plant1		Plant2		Plant3
	Cost	Return	Cost	Return	Cost	Return
1	0	0	0	0	0	0
2	1	15	2	14	1	3
3	2	18	3	18	2	7
4	4	28	4	21	–	–

 

 

 

 

 

Section – C

III)  Compulsory Question .                                                                                                                       (1×20=20)

16. The casualty room of a hospital receives between zero and six emergency calls each night according to the following probability distribution.

calls	0	1	2	3	4	5	6
probability	0.05	0.12	0.15	0.25	0.22	0.15	0.06

 

The medical team at the casualty room classifies each emergency call into one of the three categories: minor, medium or major emergency. The probability that a particular call will be each type of emergency is as below:

Emergency Type	Minor	Medium	Major
Probability	0.30	0.56	0.14

 

The type of emergency call determines the size of the medical team scheduled to treat the emergency. A minor emergency requires two person medical team, a medium emergency requires three person medical team and a major emergency requires five person medical team.

Simulate the emergency calls received for 10 nights, compute the average number of each type of emergency call each night and determine the maximum number of medical team members  that may be required on any given night.

Random Numbers:

Number of calls during ten nights:  65, 48, 08,05, 89, 06, 62, 17, 77, 68

Emergency type for each call :  71, 18, 12, 17, 89, 18, 83, 90, 18, 08,

26, 47, 94, 72, 47, 68, 60, 88, 36, 43,

28, 31, 06, 39, 71, 22, 76.

 

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