MCA II Semester [R09] Regular Examinations June 2010
Operations Research
Time: 3 Hours Max Marks: 60
Answer any FIVE questions All questions carry EQUAL marks
1.
(a) Define Operations Research.
(b) Give at least five applications of Operations Research.
(c) Explain characteristics of Operations Research.
2.
(a) Solve the following LPP using Graphical method
Maximize Z = 2x1+3x2
Subject to the constraints
x1+x2 <= 400
2x1 + x2 <= 600
&x1 >= 0, x2 >= 0
(b) What are artificial variables and give importance.
(c) Explain simplex method in detail.
3.
(a) Explain various methods to find Basic Feasible Solution to Transportations
Problems.
(b) Give mathematical definition of assignment problem.
(c) We have five jobs each of which must go through the machines A, B and C in the
order ABC. Determine the sequence that will minimize the total elapsed time
Job No 1 2 3 4 5
Machine A 5 7 6 9 5
Machine B 2 1 4 5 3
Machine C 3 7 5 6 7
4. The cost of a machine is Rs 61000 and its scrap value is Rs 1000. the maintenance cost
found from past experiences are as follows
Year 1 2 3 4 5 6 7 8
Maintenance
Cost in rs. 1000 2500 4000 6000 9000 12000 1600 20000
When should the machine be replaced?
5. A T.V repairman finds that the time spent on his jobs has an exponential distribution with
mean 30 minutes. If he repairs sets in the order in which they come in. if the arrival of
sets approximately Poisson with an average rate of 10 per 8-hour day, what is the
repairman’s expected idle time each day? How many jobs are ahead of the average set
just brought in?
6. The annual demand of an item is 3200 units. The unit cost is Rs. 6/- and inventory
carrying charges 25% per annum. If the cost of one procurement is Rs. 150/-. Determine
(a) EOQ
(b) Number of orders per year.
(c) Time between two consecutive orders.
(d) The optimal cost.
7. solve the following game
Player B
I II III
Player A I -4 6 3
II -3 -3 4
III 2 -3 4
8. Cosider the following schedule
Job :(1, 2) (1, 3) (1, 4) (2, 4) (3, 4) (4, 5)
Duration(days): 9 8 14 5 6 1
(a) Construct network diagram
(b) What is the project duration
(c) Identify critical, Non-critical activities.
(d) Critical path.
MCA II Semester [R06] Supplementary Examinations June 2010
Operations Research
Time: 3 Hours Max Marks: 60
Answer any FIVE questions All questions carry EQUAL marks
1. (a) Define LPP give example
(b) Solve the following LPP using Graphical method.
Minimize Z = 5x1 + 5/2 x2
Subject to the constraints
2x1 + 4x2 >=40
3x1 + 2x2 >=50
& x1, x2 >=0
(c) Solve the following LPP using simplex method
Maximize Z = 7x1 + 5x2
Subject to the constraints
x1+ 2x2 <= 6
4x1 + 3x2<=12
& x1, x2>0
2. (a) Define Assignment problem mathematically.
(b) Find the optimal solution of the following 5 x 4 Transportation problem
costs
10 20 5 7 10
13 9 12 8 20
4 15 7 9 30 supply
14 7 1 0 40
3 12 5 19 50
Demand 60 60 20 10
3. A machine operator has to perform three operations turning, threading and knurling on a
number of different jobs. The time required to perform these operations (in minutes) for
each job is known. Determine the order in which the jobs should be processed in order to
minimize the total time required to turn out all the jobs. Also find the minimum elapsed
time.
Job-> I II III IV V VI
Turning 3 12 5 2 9 11
Threading 8 6 4 6 3 1
knurling 13 14 9 12 8 13
4. A machine costs Rs.10, 000/-. Its operating cost and resale value are given in the table.
Determine at what time it could be replaced?
Year 1 2 3 4 5 6 7 8
Operating
Cost 1000 1200 1400 1700 2000 2500 3000 3500
Resale
value 6000 4000 3200 2600 2500 2400 2000 1600
5. In a railway marshalling yard, goods train arrive at the rate of 30 trains per day. Assume
that the inter arrival time follows an exponential distribution and the service time is also
to be assumed as exponential with mean 36 minutes. Calculate
(a) The probability that the yard is empty.
(b) The average queue length assuming that the line capacity of the yard is 9 trains
6. The demand rate of a particular item is 12, 000 units per year. The set-up cost per run is
Rs. 350/- and the holding cost is Rs. 0.20/- per unit per month. If no shortages are
allowed and the replacement is instantaneous, determine
(a) The optimum run size.
(b) The optimum scheduling period.
(c) Minimum expected annual cost.
7. (a) Explain the theory of dominance in the solution of rectangular games.
(b) Solve the game graphically whose pay off matrix for the player A is given
B
I II
I 2 4
A II 2 3
III 3 2
IV -2 6
8. What is dynamic programming and give the importance of the dynamic programming.
State and establish Bellman’s Principle of Optimality
Operations Research
Time: 3 Hours Max Marks: 60
Answer any FIVE questions All questions carry EQUAL marks
1.
(a) Define Operations Research.
(b) Give at least five applications of Operations Research.
(c) Explain characteristics of Operations Research.
2.
(a) Solve the following LPP using Graphical method
Maximize Z = 2x1+3x2
Subject to the constraints
x1+x2 <= 400
2x1 + x2 <= 600
&x1 >= 0, x2 >= 0
(b) What are artificial variables and give importance.
(c) Explain simplex method in detail.
3.
(a) Explain various methods to find Basic Feasible Solution to Transportations
Problems.
(b) Give mathematical definition of assignment problem.
(c) We have five jobs each of which must go through the machines A, B and C in the
order ABC. Determine the sequence that will minimize the total elapsed time
Job No 1 2 3 4 5
Machine A 5 7 6 9 5
Machine B 2 1 4 5 3
Machine C 3 7 5 6 7
4. The cost of a machine is Rs 61000 and its scrap value is Rs 1000. the maintenance cost
found from past experiences are as follows
Year 1 2 3 4 5 6 7 8
Maintenance
Cost in rs. 1000 2500 4000 6000 9000 12000 1600 20000
When should the machine be replaced?
5. A T.V repairman finds that the time spent on his jobs has an exponential distribution with
mean 30 minutes. If he repairs sets in the order in which they come in. if the arrival of
sets approximately Poisson with an average rate of 10 per 8-hour day, what is the
repairman’s expected idle time each day? How many jobs are ahead of the average set
just brought in?
6. The annual demand of an item is 3200 units. The unit cost is Rs. 6/- and inventory
carrying charges 25% per annum. If the cost of one procurement is Rs. 150/-. Determine
(a) EOQ
(b) Number of orders per year.
(c) Time between two consecutive orders.
(d) The optimal cost.
7. solve the following game
Player B
I II III
Player A I -4 6 3
II -3 -3 4
III 2 -3 4
8. Cosider the following schedule
Job :(1, 2) (1, 3) (1, 4) (2, 4) (3, 4) (4, 5)
Duration(days): 9 8 14 5 6 1
(a) Construct network diagram
(b) What is the project duration
(c) Identify critical, Non-critical activities.
(d) Critical path.
MCA II Semester [R06] Supplementary Examinations June 2010
Operations Research
Time: 3 Hours Max Marks: 60
Answer any FIVE questions All questions carry EQUAL marks
1. (a) Define LPP give example
(b) Solve the following LPP using Graphical method.
Minimize Z = 5x1 + 5/2 x2
Subject to the constraints
2x1 + 4x2 >=40
3x1 + 2x2 >=50
& x1, x2 >=0
(c) Solve the following LPP using simplex method
Maximize Z = 7x1 + 5x2
Subject to the constraints
x1+ 2x2 <= 6
4x1 + 3x2<=12
& x1, x2>0
2. (a) Define Assignment problem mathematically.
(b) Find the optimal solution of the following 5 x 4 Transportation problem
costs
10 20 5 7 10
13 9 12 8 20
4 15 7 9 30 supply
14 7 1 0 40
3 12 5 19 50
Demand 60 60 20 10
3. A machine operator has to perform three operations turning, threading and knurling on a
number of different jobs. The time required to perform these operations (in minutes) for
each job is known. Determine the order in which the jobs should be processed in order to
minimize the total time required to turn out all the jobs. Also find the minimum elapsed
time.
Job-> I II III IV V VI
Turning 3 12 5 2 9 11
Threading 8 6 4 6 3 1
knurling 13 14 9 12 8 13
4. A machine costs Rs.10, 000/-. Its operating cost and resale value are given in the table.
Determine at what time it could be replaced?
Year 1 2 3 4 5 6 7 8
Operating
Cost 1000 1200 1400 1700 2000 2500 3000 3500
Resale
value 6000 4000 3200 2600 2500 2400 2000 1600
5. In a railway marshalling yard, goods train arrive at the rate of 30 trains per day. Assume
that the inter arrival time follows an exponential distribution and the service time is also
to be assumed as exponential with mean 36 minutes. Calculate
(a) The probability that the yard is empty.
(b) The average queue length assuming that the line capacity of the yard is 9 trains
6. The demand rate of a particular item is 12, 000 units per year. The set-up cost per run is
Rs. 350/- and the holding cost is Rs. 0.20/- per unit per month. If no shortages are
allowed and the replacement is instantaneous, determine
(a) The optimum run size.
(b) The optimum scheduling period.
(c) Minimum expected annual cost.
7. (a) Explain the theory of dominance in the solution of rectangular games.
(b) Solve the game graphically whose pay off matrix for the player A is given
B
I II
I 2 4
A II 2 3
III 3 2
IV -2 6
8. What is dynamic programming and give the importance of the dynamic programming.
State and establish Bellman’s Principle of Optimality
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