Anna University Previous Years Question Papers
Question paper code: 40340
M.B.A. DEGREE EXAMINATION,APRIL/MAY-2015
Second semester
BA 7206 –APPLIED OPERATION RESEARCH
(Regulation2013)
Time- Three hour
Maximum mark-100
Answer all questions
PART A -10X2=20
1. State the limitation of a graphical method.
2. How dose dual simplex method differ from simplex method.
3. What is an unbalanced transportation problem.
4. Which cell will be the first cell variable in case of North Wast Cornor method and least cost method?
5. While using IPP technique,What is the fractional part of- 98/18?
6. Differentiate between pure and mixed strategies.
7. List the elements of carrying cost.
8. What do the terms uncertainty and risk refer?
9. In a store with one cashier, nine customers arrive on the average of every five minutes and the cashier can serve them ten in five minutes. Find utilisation factor.
10. If the money carries an interest rate of 10% per year, what will be the value of one rupee after two year?
PART B-5X16=80
11.(b)(i)Solve the following LPP graphically;
Minimize Z=3x+2y
Subject to x-y≤1,x+y≥3and x,y≥0.
(ii) A person wants to decide the constituents of a diet which fulfil his daily requirements of protein, fat and carbohydrate at the minimum cost. The choice is to be made from four different types of food are given below:
Food type yield per unit
Protein Fat Carbohydrate cost per unit
1 3 2 6 45
2 4 2 4 40
3 8 7 7 85
4 6 5 4 65
Minimum requirement 800 200 700
Formula the LPP for the problem .
(b) Solve the following LPP two phase single method:
Minimize Z=-4a-3b-9c;
Subject to2α+4b+6c≥15
6α+b+6c≥12
a,b,c≥0
12.(a)Solve the following transportation problem to minimize the total transportation cost for shifting the goods from the factories (A, Band C) to were houses respectively are given in the following metric:
Ware house
P Q R Availability
A 1 2 0 30
Factory B 2 3 4 35
C 1 5 6 35
Demand 30 40 30
Find the allocation so that the total transportation cost is minimum.
(or)
(b)A company has four territories and four salesman was assignment. The territories are not equally rich in their sales potential. It is estimated that a typical salesman operating in each territory would bring the following annual sales.
Territory: I II III IV
Annual sales in Rs; 60,000 50,000 40,000 30,000
The four salesman are also considered to differ in their ability ; it is estimated that working under same condition, their yearly sales would be proportionately as follows:
Salesman: A B C D
Proportion: 0.1 0.2 0.3 0.4
If the criteria is to maximize expected sales ,What is your intuitive answer and verity your answer with Hungarian method.
13.(a)(i)Find the optimum integer solution to the following LPP;
Maximize Z=3x1+7x2
Subject to 3x1+4x2≤19
3x1+6x2≤21
x1, x2 non-negative integers.
(or)
(b)(i)State the rules of dominance.
(ii)Solve the following game ;
Player B
Player A 1 7 2
6 2 7
5 1 6
14.(a)(i)Derive EOQ formula for simple inventory model with no shortages and instantaneous replenishment.
(ii)Find the optimum order quantity for the product for which the price break is given below:
QUANTITY UNIT COST
0≤q1<100 Rs 20 per unit
100≤q1<200 Rs 18 per unit
200≤q3 Rs 16 per unit
The monthly demand for the product is 400 units. The storage cost is 20%of the unit cost of the product and the cost of ordering is Rs.25.
(or)
(ii)Concisely explain the criterions used to assist decision making under uncertainty.
15.(a)(i)A TV repairman finds that the time ha spent on his an exponential distribution with means 30 minutes. If he repairs the set in the order it arrives and the arrives rate is approximately poisson , with an average rate of 10 per 8 hours day, What is the expected idle of repairman each day ?How many jobs are a head of average before the job just brought in?
(ii)A telephone exchange has two long distance operators. The telephone company finds that during the peak load long distances calls arrives in a poisson fashion at the average rate of 15 per hour. The length of services on these calls is approximately distributed with mean 5 minutes.
(1)What is the probability that subscriber will have to wait for his long distance call during the peak hour of the day?
(2)If the subscriber will wait and be serviced in turn what is the expected waiting time in queue?
(or)
(b) A machine costs Rs.15,000 and its running costs for different years are given below. Find optimum replacement period if the capital is worth 10% and the machine has no salvage value.
Year: 1 2 3 4 5 6 7
Running cost Rs:2500 3000 40000 5000 6500 8000 10000
Question paper code: 40340
M.B.A. DEGREE EXAMINATION,APRIL/MAY-2015
Second semester
BA 7206 –APPLIED OPERATION RESEARCH
(Regulation2013)
Time- Three hour
Maximum mark-100
Answer all questions
PART A -10X2=20
1. State the limitation of a graphical method.
2. How dose dual simplex method differ from simplex method.
3. What is an unbalanced transportation problem.
4. Which cell will be the first cell variable in case of North Wast Cornor method and least cost method?
5. While using IPP technique,What is the fractional part of- 98/18?
6. Differentiate between pure and mixed strategies.
7. List the elements of carrying cost.
8. What do the terms uncertainty and risk refer?
9. In a store with one cashier, nine customers arrive on the average of every five minutes and the cashier can serve them ten in five minutes. Find utilisation factor.
10. If the money carries an interest rate of 10% per year, what will be the value of one rupee after two year?
PART B-5X16=80
11.(b)(i)Solve the following LPP graphically;
Minimize Z=3x+2y
Subject to x-y≤1,x+y≥3and x,y≥0.
(ii) A person wants to decide the constituents of a diet which fulfil his daily requirements of protein, fat and carbohydrate at the minimum cost. The choice is to be made from four different types of food are given below:
Food type yield per unit
Protein Fat Carbohydrate cost per unit
1 3 2 6 45
2 4 2 4 40
3 8 7 7 85
4 6 5 4 65
Minimum requirement 800 200 700
Formula the LPP for the problem .
(b) Solve the following LPP two phase single method:
Minimize Z=-4a-3b-9c;
Subject to2α+4b+6c≥15
6α+b+6c≥12
a,b,c≥0
12.(a)Solve the following transportation problem to minimize the total transportation cost for shifting the goods from the factories (A, Band C) to were houses respectively are given in the following metric:
Ware house
P Q R Availability
A 1 2 0 30
Factory B 2 3 4 35
C 1 5 6 35
Demand 30 40 30
Find the allocation so that the total transportation cost is minimum.
(or)
(b)A company has four territories and four salesman was assignment. The territories are not equally rich in their sales potential. It is estimated that a typical salesman operating in each territory would bring the following annual sales.
Territory: I II III IV
Annual sales in Rs; 60,000 50,000 40,000 30,000
The four salesman are also considered to differ in their ability ; it is estimated that working under same condition, their yearly sales would be proportionately as follows:
Salesman: A B C D
Proportion: 0.1 0.2 0.3 0.4
If the criteria is to maximize expected sales ,What is your intuitive answer and verity your answer with Hungarian method.
13.(a)(i)Find the optimum integer solution to the following LPP;
Maximize Z=3x1+7x2
Subject to 3x1+4x2≤19
3x1+6x2≤21
x1, x2 non-negative integers.
(or)
(b)(i)State the rules of dominance.
(ii)Solve the following game ;
Player B
Player A 1 7 2
6 2 7
5 1 6
14.(a)(i)Derive EOQ formula for simple inventory model with no shortages and instantaneous replenishment.
(ii)Find the optimum order quantity for the product for which the price break is given below:
QUANTITY UNIT COST
0≤q1<100 Rs 20 per unit
100≤q1<200 Rs 18 per unit
200≤q3 Rs 16 per unit
The monthly demand for the product is 400 units. The storage cost is 20%of the unit cost of the product and the cost of ordering is Rs.25.
(or)
(ii)Concisely explain the criterions used to assist decision making under uncertainty.
15.(a)(i)A TV repairman finds that the time ha spent on his an exponential distribution with means 30 minutes. If he repairs the set in the order it arrives and the arrives rate is approximately poisson , with an average rate of 10 per 8 hours day, What is the expected idle of repairman each day ?How many jobs are a head of average before the job just brought in?
(ii)A telephone exchange has two long distance operators. The telephone company finds that during the peak load long distances calls arrives in a poisson fashion at the average rate of 15 per hour. The length of services on these calls is approximately distributed with mean 5 minutes.
(1)What is the probability that subscriber will have to wait for his long distance call during the peak hour of the day?
(2)If the subscriber will wait and be serviced in turn what is the expected waiting time in queue?
(or)
(b) A machine costs Rs.15,000 and its running costs for different years are given below. Find optimum replacement period if the capital is worth 10% and the machine has no salvage value.
Year: 1 2 3 4 5 6 7
Running cost Rs:2500 3000 40000 5000 6500 8000 10000
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