Operations Research For Business Decisions

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.

 

St. Joseph’s College of Commerce (Autonomous)

End Semester Examination- APRIL 2014

MIB – II Semester

OPERATIONS RESEARCH FOR BUSINESS DECISIONS

Duration: 3 Hrs                                                                                         Max. Marks: 100

 

SECTION – A

 

1. I) Answer any SEVEN Each carries 5 marks.                        (7 x 5 = 35)

 

1. Explain with reasons which of the following statements are true or false:
2. a) Emotions and guesswork is not part of Operation Research
3. b) The purpose of using simulation technique is to understand properties and operating characteristics of complex real life problems.
4. c) An assignment problem cannot have multiple optimal solution.

 

2. The Mapple Store sells Mapple Computers and printers. The computers shipped are in 12 cubic foot boxes and printers in 8 cubic foot boxes. The Mapple store estimates that at least 30 computers can be sold each month and the number of computers sold will be at least 50% more than the number of printers. The computers cost the store $1000 each and are sold for a profit of $1000. The printers cost the store $300 and are sold for a profit of $350.the store has a storeroom that can hold 1000 cubic feet and can spend $70,000 each month on computers and printers. How many computers and how many printers should be sold each month to maximize profit? What is the maximum profit? Solve by graphical method.

 

3. Define Operation Research. Explain the methodology of OR.

 

4. Imagine yourself to be the Executive Director of a 5 Star hotel which has four banquet halls that can be used for all functions including weddings. The halls were all the same size and facilities in each hall differed. During a heavy marriage season, 4 parties have approached you to reserve a hall for the marriage to be celebrated on the same day. These marriage parties were told that the first choice among these halls would cost Rs10, 000 for the day. They were also required to indicate the second, third and fourth preferences and the price they were willing to pay. Marriage party A and D indicated they were not interested in Halls 3 and 4. Other particulars are given in the table below:

 

MARRIAGE PARTY	REVENUE  HALL
	1	2	3	4
A	10,000	9000	X	X
B	8000	10,000	8000	5000
C	7000	10,000	6000	8000
D	10,000	8000	X	X

Decide on an allocation that will maximize the revenue of the hotel.

 

5. Arrival of cars at a filling station is considered to be Poisson with an average time of 4 min in between one arrival and the next. Service time is considered to be poison with an average time of 3 min. the length of filling is assumed to be distributed exponentially with mean of 0.05 hours.

 

1. a) What is the arrival rate?
2. b) What is the service rate?
3. c) What is the equipment utilization rate?
4. d) What is the average time an arrival spends in the system (waiting and servicing time)?

 

6. Solve the game whose pay-off matrix is given below:

PLAYER A	PLAYER B
	B1	B2	B3	B4
A1	1	7	3	4
A2	5	6	4	5
A3	7	2	0	3

 

7. A project consists of 9 jobs A to I with the following precedence relationships and estimates of time. Draw a project network and find the critical path with project duration

JOB	A	B	C	D	E	F	G	H	I
PREDECESSOR	–	–	A,B	A,B	B	D,E	C,F	D,E	G,H
DURATION(DAYS)	15	10	10	10	5	5	20	10	15

 

8. The occurrence of rain in a city on a day is dependent upon whether or not it rained on the previous day. If it rained on the previous day the rain distribution is given by

EVENT	PROBABILITY
NO RAIN	0.50
1 CM	0.25
2CM	0.15
3CM	0.05
4CM	0.03
5CM	0.02

 

If it did not rain the previous day, the rain distribution is given by:

EVENT	PROBABILITY
NO RAIN	0.75
1CM	0.15
2CM	0.06
3CM	0.04

 

Simulate the city’s weather for 10 days and determine by simulation the total days without rain as well as the total rainfall during the period. Use the following: 67, 63, 39, 55, 29, 78, 70, 06, 78, 76 for simulation. Assume that for the first day of the simulation it had not rained the day before.

 

9. Medicare hospital has the following minimum daily requirement for nurses

PERIOD	CLOCK TIME (24 HRS)	MINIMAL NUMBER OF NURSES REQUIRED
1	6 am – 10 am	2
2	10 am –  2 pm	7
3	2 pm – 6 pm	15
4	6 pm – 10 pm	8
5	10 pm – 2 am	20
6	2 am – 6 am	6

 

Nurses report to the hospital at the beginning of each period and work for 8 consecutive hours. The hospital wants to determine the minimal number of nurses to be employed so that there will be sufficient number of nurses available for each period. Formulate this as a linear programming problem.

 

10. Define any five terms :
11. Degeneracy b. Duality       c. Reneging           d. Unbounded solution
12. Dangling Error f. Saddle point

 

SECTION-  B

1. II) Answer any THREE questions. Each carries 15 marks.                             (3×15 = 45)

 

11. A company manufactures two products A and B. Both products are processed on two machine centres, M1 and M2.

PRODUCTS	HOURS REQUIRED PER UNIT
	M1	M2	PROFIT
A	1	3	30
B	2	2	20
CAPACITY	80	120

Solve the problem using simplex method to determine number of units of A and B to be produced per week to maximize profit. Is there an alternate solution? If yes, find it.

12. National Oil Co. has three refineries and 4 depots. Transportation costs per ton and requirements are given below:

	D1	D2	D3	D5	CAPACITY
P1	5	7	13	10	700
P2	8	6	14	13	400
P3	12	10	9	11	800
REQUIREMENT	300	600	700	400

Determine optimal allocation of output.

 

13. With a view to improving the quality of customer services, a Bank is interested in  making an assessment of the waiting time of its customers coming to one of its branches located in a residential area. This branch has only one tellers counter. The arrival rate of the customer and the service rate of the teller is given below:

Time between two consecutive arrivals of customers( in min)	Probability
3	0.17
4	0.25
5	0.25
6	0.20
7	0.13

 

Service time by the teller (in min)	Probability
3	0.10
4	0.30
5	0.40
6	0.15
7	0.05

You are required to simulate 10 arrivals of customers in the system starting from 11 am ans show the waiting time of customers and idle time of the teller.

Use the following random numbers taking the first two random numbers in two digits each for the first trial and so on: 11,56,23,72,94,83,83,02,97,99,83,10,93,34,33,53,49,94,37 and 97.

 

14. Define an OR model. Discuss the various classification schemes of models.

 

15. What is game theory? Explain with examples the concept of dominance in game theory. What are the major limitations of game theory?

 

 

Section – C

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

 

16. A construction company is preparing a PERT network for laying the foundation of a new art museum. Given the following set of activities, their predecessor requirements and three time estimates of completion time:

Activities	Duration
1-2	3
1-3	8
2-4	9
3-5	6
4-5	0
4-6	10
4-7	14
5-7	11
7-9	10
6-8	5
8-10	4
9-10	1

 

REQUIRED:

 

1. Draw the CPM Network.
2. Compute the total float for each activity and determine the critical path using forward pass 7 backward pass

 

 

 

 

1.      JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

End Semester Examinations – MARCH / APRIL 2014

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)

 

• A) Explain the rules for constructing a dual.

 

1500. B) M/s Vikram Engineering Works have obtained a large contract for the supply of an alloy steel. The alloy needs three metals X, Y and Z. If the minimum requirement of the metals per week would be: 12 units of X, 10 units of Y and 14 units of Z. The metals are available from dealers who supply them in standardized boxes containing the metals in three different proportions. The boxes are called by code numbers: 221, 321 and 421 respectively. Box 221 contains 1 unit of X, 2 units of Y and 1 unit of Z. Box 321 contains 3 units of X, 2 units of Y and 1 unit of Z whereas Box 421 contains 1 unit each of X and Y and 5 units of Z. The cost of one Box of type 221,321 and 421 is respectively, Rs 1200, Rs 900 and Rs 1500.

Draft the problem as a linear programming problem and also fine its dual.

 

2. Define Operation Research. Explain the main phases of an OR study.

 

3. Maxi Taxi Service operates every day four routes with four taxies and the relevant data is given below:

Trucks	Routes
	A	B	C	D
1	5.2	5.5	5.0	5.6
2	4.9	5.1	5.2	5.4
3	4.8	5.2	4.9	5.3
4	5.0	5.0	5.2	5.4
Distance to be covered	220	320	360	250

The table contains the kms per litre of diesel consumption by each of the taxies when run is given in the four routes. Find out the assignment of taxies to routes in order to reduce the consumption of diesel per day.

 

4. What are the various methods to develop the initial feasible solution to a transportation problem? Give the steps involved in VAM. Explain with the help of an example.

 

5. A branch of Punjab National Bank has only one typist. Since the typing work varies in length (no. of pages to be typed), the typing rate is randomly distributed approximating a Poisson distribution with mean service rate of 8 letters per hour. The letters arrive at a rate of 5 per hour during the entire 8 hour work day. If the type writer is valued at Rs 1.50 per hour, determine
6.  a) Equipment utilization
7. b) Average system time
8. c) Average idle time cost of typewriter per day

 

6. Use graphical method to solve the following problem

Max Z = 7x₁+ 3x₂

Subject to:

x₁ + 2x₂> 3

x₁ +  x₂< 4

0 < x₁< 5/2

0< x₂< 3/2

And x₁, x₂> 0

 

7. Define dynamic programming with suitable examples. List and explain the terminologies of dynamic programming problem.

 

8. Explain the following terms:
9. i) linear programming ii) surplus variable iii) prohibited assignment
10. iv) queue discipline  v) collusion

 

9. A Production Manager is planning to produce a new product and he wishes to estimate the raw material requirement for that product. On the basis of usage for similar product introduced previously, he has developed a frequency distribution of demand in tonnes per day for a two month period. Use this data to simulate the raw material usage requirements for 7 days.

Random numbers are: 27,13,80,10,54,60,49,78,66,44

Demand tonnes/day      10      11        12        13        14        15        total

Frequency no. of days   6       18        15        12        6          3          60.

 

10. A company has three production facilities S1, S2 and S3 with production capacity of 7,9 and 18 units( in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s)per week respectively. The transportation costs ( in Rs)per unit between factories and warehouses per unit between factories and warehouses per unit between factories and warehouses per unit between factories and warehouses are given in the table below

	D1	D2	D3	D4	CAPACITY
S1	19	30	50	10	7
S2	70	30	40	60	9
S3	40	8	70	20	18
DEMAND	5	8	7	14	34

Formulate this transportation problem as an LP model to minimize cost.

 

SECTION –  B

 

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

11. A firm has a single channel service station with the following arrival and service time probability distribution:

Inter arrival Time (min)	Probability	Service time (min)	Probability
10	0.10	5	0.08
15	0.25	10	0.14
20	0.30	15	0.18
25	0.25	20	0.24
30	0.10	25	0.22
		30	0.14

The customer’s arrival at the service station is a random phenomenon and the time between the arrivals varies from 10 min to 30 minutes. The service time varies from 5 min to 30 min. the queuing process begins at 10 am and proceeds for nearly 8 hours. An arrival goes to the service facility immediately if it is free. Otherwise it will wait in a queue. The queue discipline is first come- first serve.

If the attendants wages are Rs 10 per hour and the customers waiting time costs Rs 15 per hour then would it be an economical proposition to engage a second attendant? Use the following random numbers, the first for arrival and second for service and so on: 20, 26, 73,43, 30, 98, 99, 87, 66, 58, 83, 90, 32, 84, 75, 60, 04,08, 15, 50, 29, 37, 62, 42, 37, 28, 68, 84, 94, 65.

 

12. A Cheese Company has factories F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units respectively. Weekly warehouse requirements are 180, 120 and 150 units respectively. Unit shipping costs in RS are as follows:

	Warehouse
Factory		W1	W2	W3	SUPPLY
	F1	16	20	12	200
	F2	14	8	18	160
	F3	26	24	16	90
	DEMAND	180	120	150	450

 

Determine the optimal distribution for this company to minimize total shipping costs. Use North West Corner rule to find initial solution.

 

13. Mc Donald’s chain wants to build four stores.in the past, the chain has used six different construction companies and having been satisfied with each, has invited each to bid on each job. The final bids ( in 000 rupees) were as shown in the following:

STORE	CONSTRUCTION COMPANIES
	1	2	3	4	5	6
1	853	900	875	824	891	913
2	789	845	994	804	893	884
3	820	313	285	665	804	1097
4	843	346	862	833	850	855

 

Since MC Donald’s wants to have each of the new stores, ready as quickly as possible, it will award, at most one job to a construction company. What assignment results in minimum total cost to the fast food chain?

 

14. The extension counter of the Citizen’s bank in the premises of a state university has one drive-in counter.it is estimated that cars arrive according to Poisson distribution at the rate of 2 every 5 minutes and that there is enough space to accommodate a line of 10 cars. Other arriving car can wait outside this space, if necessary. It takes 1.5 minutes on an average to serve a customer, but the service time actually varies according to an exponential distribution. You are required to find:

 

1. Proportion of time the facility remains idle
2. The expected number of customers waiting but currently not being served at a particular point of time
3. The expected time a customer spends in the system and
4. The probability that the waiting line will exceed the capacity of the space leading to the drive-in counter.

 

15. Discuss the important techniques used under operation research for business decisions.

 

Section – C

 

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

 

16. A company produces three products P1, P2 and P3 from two raw materials A and B, and labor L. one unit of product P1 requires one unit of A,3 units of B and 2 units of labor.one unit of product P2 requires 2 units of A and B each and 3 units of L, while one unit of P3 requires 2units of A, 6 units of B and 4 units of L. The company has a daily availability of 8 units of A, 12 units of B, and 12 units of L. It is further known that the unit contribution margin for the products is Rs 3, 3 and 5 respectively for P1, P2 and P3.

Formulate this problem as a linear programming problem and then solve it to determine the optimum product mix. Is the solution obtained by you unique? Identify an alternate optimum solution if any.

 

 

 

ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – APRIL 2015
m.com – ii  semester
P111201: OPERATIONS RESEARCH FOR BUSINESS DECISIONS
Duration: 3 Hours                                                                                             Max. Marks: 100
SECTION – A
I)	Answer any SEVEN questions.  Each carries 5 marks.                                    (7×5=35)
	1.	The Costs and Selling Prices per unit of two products manufactured by a Company are as under:   Product A (Rs) Product B B(Rs) Selling Price 500 450 Variable Cost Direct Materials ( Rs. 25 per kg.)    100 100   Direct Labour  ( Rs. 20 per hour) 80 40   Painting (Rs. 30 per hour) 30 60   Variable Overheads 260 210 Total Costs 470 410  Profit 30 40 In any month, the maximum availability of inputs is limited to the following: Direct Materials – 480 kgs, Direct Labour Hours – 400 hours and Painting Hours – 200 hours. Formulate a Linear Programming Problem to determine the Production Plan which Maximizes the profit. (Do not solve)
	2.	Explain the Dynamic Programming Approach of solving an OR problem. Briefly explain any three applications of DPP.
	3.	Write the Dual of the following LPP Min Z= 3x + 4y + 8Z Subject to, 2x + y +10z ≥ 50 x + y = 5 x ≤ 3 Where x, y, z ≥ 0
	4.	Discuss  the significance of introducing slack, surplus and artificial variables in Simplex Method? What meaningful information can be derived from them?
	5.	A  hospital  pays  nurses for 40 hours a week. One nurse is assigned to one patient. The cost per hour for each of the nurses is given below: (i)                 Find the nurse-patient combination to minimize cost to the hospital. (ii)              How much does each nurse earn per week? Nurse Patient W X Y Z K 10 10 30 40 L 30 10 20 40 M 20 30 20 40 N 50 50 50 50
	6.	Find the initial solution using NWCM and LCM for the following transportation problem.      Toà From A B C Supply X 7 3 4 2 Y 2 1 3 3 Z 3 4 6 5 Demand 4 1 5
	7.	A belt snapping for conveyors in an open cast mine occur at the rate of 2 per shift. There is only one hot plate available for vulcanising, and it can  vulcanise on an average 5 belts snap per shift. (a)   What is the probability that when a belt snaps, the hot plate is readily available. (b)   What is the probability of having exactly 3 belts waiting for service in the system? (c)    What is the average waiting time plus vulcanising time?
	8.	A Car Rental Agency has collected the following data on the demand for five-seater vehicles over the past 50 days. Daily Demand 4 5 6 7 8 No of days 4 10 16 14 6 The Agency has only 6 cars currently. Use the following 5 Random Numbers to generate 5 days for the Rental Agency. Random nos: 15, 48 ,71 , 56, 90 What is the average number of cars rented per day for the 5 days? How many rentals will be lost over the 5 days?
	9.	Explain any five OR techniques mentioning their areas of application.
	10.	How do you deal with the following conditions while solving a Transportation Problem – Degeneracy, Unbalance, Prohibited Route.
SECTION – B
II)	Answer any THREE questions.  Each carries 15 marks.                                (3×15=45)
	11.	Solve the following LPP by Big M Method. Max Z = 10x + 12y Subject to, x + y = 5 x  ≥ 2 y  ≤ 4 where x, y ≥ 0
	12.	Plot the graph of the LPP given below  and identify the optimum solution Max Z = 0.1 x + 0.2 y Subject  to constraints, x + y ≤ 10 x ≤ 7 y  ≤ 7 -2x + 3y ≤ 0 Where x, y ≥ 0
	13.	The transportation cost matrix for a given situation for supply of the commodity from sources A, B, C to the points of usage P, Q and R is given below. Work out the optimal cost solution for the problem using Vogel’s Approximation method and Modified distribution method. Does the problem have multiple solution . If yes find the solution.   P Q R Supply A 4 8 8 76 B 16 24 16 82 C 8 16 24 77 Demand 72 102 41
	14.	A marketing manager has five salesmen and five sales districts. Considering the capabilities of the salesmen and nature of districts, the marketing manager estimates that sales per month (in thousand rupees) for each salesman in each district would be as follows – Salesmen Districts   A B C D E 1 32 38 40 28 40 2 40 24 28 21 36 3 41 27 33 30 37 4 22 38 41 36 36 5 29 33 40 35 39 Find the assignment of salesmen to districts that will result in maximum sales.
	15.	A departmental store has a single cashier. During the rush hours, customers arrive at the rate of 20 customers per hour. The average number of customers that can be processed by the cashier is 24 per hour. Assume that the conditions for the use of single channel queuing model apply. What is the (a)   Probability that the cashier is idle? (b)   Average number of customers in the queuing system? (c)    Average time a customer spends in the system? (d)  Average number of customers in the queue? (e)   Average time a customer spends in the queue waiting for service?
SECTION – C
III)	Case Study                                                                                                              (1×20=20)
	16.	ABC Company is considering the question of marketing a new product. The fixed cost required in the project is Rs. 4,000. Three factors are uncertain viz., the Selling Price, Variable Cost and Annual Sales Volume. The product has a life of only one year. The management has the data on these three factors as under.   Selling Price (Rs) Probability Variable Cost (Rs) Probability Sales Volume (Units ) Probability 3 0.20 1 0.30 2,000 0.30 4 0.50 2 0.60 3,000 0.30 5 0.30 3 0.10 5,000 0.40   Simulate the average profit for the above project on the basis of 5 trials.   Random no for selling price 81 04 67    10   39 Random no for Variable cost 32 46 25 40   68 Random no for Sales Volume (units) 60 31 24 02   08