Question 1: Define operations research. What is the relation between Quantitative Analysis and Computer Information System? Also, discuss the various quantitative analysis tools.
Question 2: What do you understand by linear programming? What are its various components and assumptions? Give a few applications of linear programming in day-today life.
Question 3: Solve the following LP Problem
Minimize Z = 6x1 + 5x2
Subject to:
4x1 + 8x2 ≥ 80 Constraint 1
6x1 + 4x2 ≥ 100 Constraint 2
x1, x2 ≥ 0 Non-negative constraint
Question 4: For the following initial basic feasible solution, conduct the optimality test and calculate minimum transportation cost.
Question 5: Elaborate on the different types of service system and queue structure.
Question 6: In a production department of a company, components have to be processed on Machine A first and then on machine B. The time taken to process on two machines varies with the following probability distribution:
|
Time on Machine A (minutes)
|
Probability
|
Time on Machine B
(minutes)
|
Probability
|
|
2
|
0.10
|
3
|
0.10
|
|
3
|
0.30
|
4
|
0.20
|
|
4
|
0.40
|
5
|
0.30
|
|
5
|
0.20
|
6
|
0.30
|
|
|
|
7
|
0.10
|
Using simulation technique and the ordered pair of random numbers, first for machine A and second for machine B, find the total idle time on both the machines. Random numbers: (36,28), (91,90), (41,09), (95, 04) and (92, 01).
Question 7: Explain the rules involved in construction of network diagram and what are the special cases where dummy activity are considered. Also, state the advantages, disadvantages of CPM/PERT along with their applications.
Question 8: Discuss the resource allocation and smoothing concept. Also, give the procedure of resource smoothing.
Question9: What do you understand by decision theory? What steps are involved in decision making? Also, discuss the decisions taken on basis of several rules or criteria.
Question 10: Solve the following game, whose payoff matrix is given below.
|
Firm A
|
Firm B
|
|
B1
|
B2
|
B3
|
|
A1
|
8
|
-4
|
-2
|
|
A2
|
9
|
17
|
16
|
|
A3
|
10
|
20
|
-5
|
Question 11: Discuss the nature and characteristics of operations research along with its application in different areas.
Question12: Hero cycles operate two assembly lines, P and Q. Each line is used to assemble the components of three types of bicycles namely, standard, supreme, and deluxe. The expected daily production on each line is as follows:
|
Model
|
Line P
|
Line Q
|
|
Standard
|
3
|
1
|
|
Supreme
|
1
|
1
|
|
Deluxe
|
2
|
6
|
The daily running costs for line P and Line Q are Rs.6000 and Rs.4000 respectively. The company has to fulfill the pending production order of at least 24 standard, 16 supreme, and 48 deluxe cycles. Determine the number of days required to fulfill the requirements with the least cost.
Question 13: Formulate the dual of the given primal:
Minimize Z = 2x1 + 5x2 + 8x3
Subject to:
6x1 + 8x2 + 4x3 ≤ 96 Constraint 1
2x1 + x2 + 2x3 ≥ 40 Constraint 2
5x1 + 3x2 + 2x3 = 60 Constraint 3
x1, x2, x3 ≥ 0
Question14: Elaborate on the different method of finding Initial Basic Feasible (IBF) solution?
Question 15: At a barber's shop, there is only one barber and the customers have an arrival rate of 2.5 customers per hour, and haircuts are given with the service rate of 5 per hour. Use the Poisson arrivals and Exponential Service Time's Model to find the operating characteristics of the system.
Question 16: Define Simulation. Outline the simulation procedure for the inventory system of a retail store.
Question 17: Explain the rules involved in construction of network diagram and what are the special cases where dummy activity are considered. Also, state the advantages, disadvantages of CPM/PERT along with their applications.
Question 18: The time and cost estimates of different activities of a project and their precedence relationships are given below:
The indirect costs amount to '1000 per week. Crash the project to optimal extent.
|
Activity
|
Immediate Predecessor
|
Normal time (NT)
In weeks
|
Normal Cost
('00 Rs.)
(NC)
|
Crash time (CT)
(In weeks)
|
Crash Cost
('00 Rs.)
(CC)
|
|
A
|
--------
|
6
|
100
|
4
|
140
|
|
B
|
--------
|
4
|
50
|
3
|
80
|
|
C
|
A
|
3
|
40
|
2
|
50
|
|
D
|
B
|
8
|
10
|
3
|
60
|
|
E
|
B
|
14
|
90
|
6
|
130
|
|
F
|
C,D
|
8
|
70
|
4
|
80
|
The indirect costs amount to '1000 per week. Crash the project to optimal extent.
Question 19: What do you understand by decision theory? What steps are involved in decision making? Also, discuss the decisions taken on basis of several rules or criteria.