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MCA Degree Model Question Paper Bharathiar University Second Semester
This resource about Model question paper for MCA students of bharathiar University and affiliated colleges of Bharathiar university, Coimbatore
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Subject :OPERATIONS RESEARCH (33E)
Course : M.C.A.
Semester : Third
Time : 3 Hours
Max: 75 Marks
Section – A (10 * 1 = 10 Marks)
Answer all Questions.
1. What do you meant by an artificial variable?
2. What is the dual of dual in a L.P.P?
3. When a Transportation Problem is said to be an unbalanced one?
4. What is an Impossible Assignment?
5. What is an inventory?
6. Define Lead-time.
7. State the need for Replacement.
8. What do you mean by present worth factor?
9. Explain the term service channel in queuing model.
10. Define the term " Arrival Rate"
Section – B ( 5 * 5 = 25 Marks)
Answer all Questions.
11. a). A company produces two types of leather belts A and B. A is of superior quality and B is of inferior quality. The respective profits are Rs.10 and Rs.5 per belt. The supply of raw material is sufficient for making 850 belts per day. For Belt A, special type of buckle is required and only 500 are available per day. There are 700 buckles available for belt B per day. Belt A needs twice as much time as that required for belt B and the company can produce 1000 belts per day (both A and B combined). Formulate a L.P.P for the above problem.
(OR)
b). Solve the following LPP graphically:
Maximize Z = 120 X1 + 100 X2
Subject to
10 X1 + 5 X2 ≤ 80, 6 X1 + 6 X2 ≤ 66,
4 X1 + 8 X2 ≥ 24, 5 X1 + 6 X2 ≤ 90
and X1, X2 ≥ 0
12. a). Find the initial basic feasible solution to the following transportation problem using Vogel's
Approximation Method
From D1 D2 D3 Supply
O1 6 8 4 14
O2 4 9 8 12
O3 1 2 6 5
Demand 6 10 15
(OR)
b). Solve the following Assignment Problem.
A B C D
I 10 25 15 20
II 15 30 5 15
III 35 20 12 24
IV 17 25 24 20
13. a). Explain about various costs involved in inventory with example.
(OR)
b).The demand for a particular item is 18,000 units per year. The holding cost per unit is Rs.1.20 per year and the cost of one procurement is Rs. 400.No shortages are allowed and determine the following:
(a) Optimum order quantity
(b) The time between orders
(c) The number of orders per year
(d) The total cost if the cost of one unit is Re. 1.00
14. a). Following table gives the running costs per year and resale price of a certain equipment whose
Purchase price is Rs. 8,000.
Year : 1 2 3 4 5 6 7 8
Running Costs(Rs.) 1,000 1,300 1,700 2,200 2,900 3,800 4,800 6,000
Resale Value(Rs.) 4,000 2,000 1,200 600 500 400 400 400
At what age is a replacement due? Page 1/3
b). Construct the network diagram for the following activities.
A < D,E; B,E,F < H; C < F,I; D < G; G,H,I < J; J < K; K < L.
15. a). List out the various characteristics of a queuing system.
(OR)
b). A TV repairmen finds that the time spent on his jobs has a exponential distribution with mean 30 minutes. If he repairs the sets in the order in which they came in, and if the arrival of sets is approximately poison with an average rate of 10 per 8 hours day. What is repairman's expected idle time each day? How many jobs are ahead if the average set just brought in?
Section – C ( 5 * 8 = 40 Marks)
Answer all Questions.
16. a). Solve the following LPP by Simplex method:
Maximize Z = 3x1 + 2x2 + 5x3
Subject to
x1 + 2x2 + x3 ≤ 40
3x1 + 2x3 ≤ 60, x1 + 4x2 ≤ 30
and x1 , x2, x3 ≥ 0
(OR)
b). Use dual simplex method to solve the following problem:
Minimize z = 10x1 + 6x2 + 2x3
Subject to
-x1 + x2 + x3 ≥ 1
3x1 + x2 - x3 ≥ 2
and x1 , x2, x3 ≥ 0
17. a). Obtain an optimal basic feasible solution for the following transportation problem.
D1 D2 D3 D4 Available
O1 6 1 9 3 70
O2 11 5 2 8 55
O3 10 12 4 7 90
bi 85 35 50 45
(OR)
b). Solve the following Assignment Problem to maximize the overall return.
I II III IV V VI
1 9 22 58 11 19 17
2 43 78 72 50 63 48
3 41 28 91 37 45 33
4 74 42 27 49 39 32
5 36 11 57 22 25 18
6 13 56 53 31 17 28
18. a). The demand for an item is 18,000 units/year. The cost of one purchase is Rs.400. The holding cost is
Rs.1.2 per unit per year. The item cost is Re.1 per item. The shortage cost is Rs.5 per unit per year.
Determine:
(i) The optimum order quantity
(ii) The time between orders
(iii) The number of orders per year
(iv) The optimum shortage
(v) The maximum inventory
(vi) The time of items being held
(vii)The Time of shortages
(vii)The optimum annual cost
(OR)
b). Find the optimal order quantity for a product for which the price breaks are as follows:
Quantity Unit cost
0 ≤ Q1 < 100 Rs. 20.00
100 ≤ Q 2 < 200 Rs. 18.00
200 ≤ Q 3 Rs. 16.00
The monthly demand for the product is 400 units, the cost of storage is 20% of the unit cost and ordering cost is Rs. 25.00 per order.
Page 2/3
19. a) A manufacture is offered two machines A and B. A is priced at Rs. 5,000 and running costs are
estimated at Rs. 800 for each of the first five years, then increasing by Rs. 200 per year in the sixth
and subsequent years. Machine B, which has the same capacity of A, costs Rs. 2,500 but will have
running costs of Rs. 1,200 per year for six years, and then increasing by Rs. 200 per year thereafter.
If money is worth 10% per year, Which machine should be purchased?
(OR)
b). A project is composed of 12 activities, the time estimates for which are given below:
Activity tm to tp
1-2 2 1 3
2-3 2 1 3
2-4 3 1 5
3-5 4 3 5
4-5 3 2 4
4-6 5 3 7
5-7 5 4 6
6-7 7 6 8
7-8 4 2 6
7-9 6 4 8
7-8 2 1 3
(i) Draw the network diagram for the project.
(ii) Calculate slacks for each node
(iii) Determine the critical path
(iv) What is the probability of completing the project in 30 days?
20. a). Arrivals at a telephone booth are considered to be poison, with an average time of 10 minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially with mean 3 minutes.
(i) What is the probability that a person arriving at the booth will have to wait?
(ii) What is the average length of queue?
(iii) What is the average length of system?
(iv) What is the average number of customers in the system?
(OR)
b). A super market has two girls ringing up sales at the counters. If the service time for each customer
is exponential with mean 4 minutes and if people arrive in a poison fashion at the rate
of 10 per hour.
(i) What is the probability of having to wait for service?
(ii) What is the average length of queue?
(iii) What is the average length of system?
(iv) What is the average number of customers in the Queue?
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