Operation Research Management
 Section I is compulsory
 Attempt any three questions from Section II
 Use of Simple calculator is allowed.
Section I
Q1. Answer the following questions briefly: (3 X 5 = 15 Marks)
 What are the limitations of Linear Programming?
 Explain Slack Variable in Simplex .
 Why is a nondegenerate solution a prerequisite for optimality test of transportation solution?
 What is Network Analysis?
 What is meant by project crashing?
Q2. A company has three plants and three warehouses. The supply and demand in units and corresponding transportation costs in Rs. per unit are given below. On the basis of the past experience, the following transportation schedule has been finalised.
Plant 
Warehouses (Transportation costs in Rs./unit) 
Sypply (in Units) 

I 
II 
III 

A 
40 
70 
90 
300 

(300) 

B 
12 
8 
30 
400 

(300) 
(100) 

C 
60 
90 
45 
200 

(200) 

Demand (in Units) 
300 
300 
300 
900 
 Improve the above solution to optimality. (7 Marks)
 Study the solution found by you and answer the following questions with justification:
i. Is there any alternate optimal solution? (2 Marks)
ii. Find the total minimum transportation cost. (2 Marks)
iii. If the route C to II is used, by how much amount the total transportation cost would go up for every unit transported? (2 Marks)
iv. What should be the minimum decrease in the unit cost of the cell A –II so that the company will be using this route? (2 Marks)
Section II
Q3. A company manufactures two products A & B. Both products are processed on two machines M1 & M2.
Products / Machines 
M1 
M2 
A 
6 hours / unit 
2 hours / unit 
B 
4 hours / unit 
4 hours / unit 
Availability 
7200 hours / month 
4000 hours / month 
Profit per unit for A is Rs.100 and for B is Rs.80. Find out monthly production of A and B to maximise profit using the graphical method or the simplex method. (10 Marks)
Q4. In a factory there are 5 employees and 5 jobs are to be completed on one to one basis. Time required in minutes is given for each employee job combination. Find the optimal assignment of employees and jobs to minimize the total time. (10 Marks)
Jobs

A 
B 
C 
D 
E 
Employees 

I 
160  130  175  190  200 
II 
135  120  130  160  175 
III 
140  110  155  170  185 
IV 
50  50  80  80  110 
V 
55  35  70  80  105 
Q5. A small project consists of seven activities. Optimistic time, most likely time and pessimistic time estimates are given for each activity.
Activity 
Preceding Activity 
Time in Days 

Optimistic 
Most Likely 
Pessimistic 

A 
– 
2 
5 
8 
B 
– 
2 
5 
14 
C 
A 
4 
6 
14 
D 
A 
5 
7 
15 
E 
B,C 
2 
3 
10 
F 
D 
3 
3 
3 
G 
E 
1 
2 
3 
 Draw the PERT Network and find expected completion time of the project.
 What is the probability that the project will be completed in?
 18 days
 21 days
 16 days
 If the project manager wants an assurance of 95% that the project is completed on time, how many days before the scheduled date he should start the project. (10 Marks)
(Area under standard normal curve for z=1.26 is 0.3962 and for z=0.84 is 0.2996.
For Probability 0.4505 value of z=1.65)
Q6. A dealer buys a product from a manufacturer at a cost of Rs.70 per unit. He sells the product to retailers at Rs.100 per unit. The product has an expiry date of one year. At the end of the year, unsold quantity of the products can be sold as scrap at a price of Rs.20 per unit.
The market demand fluctuates between 6 to 10 units. The order for the product should be placed at the beginning of the year only. The dealer wants to decide how many units to order. Prepare payoff table and regret table. (5 Marks)
If the following probabilities are assigned to various possible events:
Event Probability
E1: Demand = 6 units P1 = 0.1
E2: Demand = 7 units P1 = 0.2
E3: Demand = 8 units P1 = 0.3
E4: Demand = 9 units P1 = 0.25
E5: Demand = 10 units P1 = 0.15
Find:
 Expected Monetary Value (2 Marks)
 Expected Opportunity Loss (1 Mark)
 Expected Pay off with PI (1 Mark)
 Expected value of PI (1 Mark)
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