Roll No. ......................

ToGI No. of Questions: 09J~'1 \) l

[Total No. of Pages: 03 ..

B.Tech. (Sem. - 6th)OPERATION RESEARCH

SUBJECT CODE ~ CS - 326 (Elective - I)

Paper ID : [A0476] .

INotc : Plcase fill sub,icet eodc and papcr ID OJ)0 MRJ

Time: 03 Hours

Instruction to Candidates:

Q1)

1VlaximumMarks: 60

I)

2)

3)

Section - A is Compulsory.. '

Attempt any Four questions from Section - B.Attempt any Two questions from Section - t.

Section -A

(10 X 2 =20)

a)

b)

Define operation research and enlist its scope.

c)

Write a note on degeneracy in Simplex Method.

Discuss briefly anyone method to be used to obtain initial basic feasiblesolution a transportation model.

d) Define assigmnent problem. How it can be represented in a mathematicalform? '

e) Define the theory of Games. Discuss the various characteristics ofCompetitive Games.

Discuss briefly the Simulation. Why,there is need for simulation?f)

g) What is goal progranuning? Distinguish it from linear programming.

h)

i)

What is PERT & CPM? Write the objectives of CPM & PERT.

List & explain briefly, the assumptions of linear programming problems.

.i) What is meant by the term 'feasible region'? Why this must be a welldefined boundary for maximization problem?

1\;/-50611859} R T.O.

Section - B

(4 X 5 =}20)

Q2) Discuss the various phases in solving operation research problem.

Q3) A person wants to decide the constituents of a diet which ~ill fulfil his dailyrequirements of proteins, fats and carbohydrates at the minimum cost. Thechoice is to be made frgm four different types of foods. The yields per unit ofthese foods as given in the following table:

Q4) Maximize, by using graphical method, the objective function Z = 2Xl+.3.x2,subject to constraint Xj + X2~ 1, 3xj +X2 ~4, xl' X2 ~O.

Q5) Solve the fonowing LP problem using simplex niethod:

- Maximize Z = 5xj'+ 3X2+ txv subject to Xj + X2+ 2X3 ~ 22, 3xj + 2x2 + X3 ;;; 26,Xj + X2+ X3 ~ 18, xl' X2 & X3 ~ O.

Q6) Define event float & activity float. Define and write the equations of

(a) Total float (b) Free float (c) Independent float

Section- C

(2 X 10 =-20)

Q7) (a) . What is the principle of duality in linear programming? Explain itsadvantages.

(b) \Vhichcompetitive situation is called a game? What is the maximincriterion of optimality? What are the assumptions inade in the th~OlYofgames? State also the major limitations of game theory.

v

M-506 2.

Food Type Yield per unit Cost/unit,

Proteins Fat Carbohydrates (Rs.)

1 3 2 7 45

2 4 3 6 40

3 7 6 . 5 85

4. 6 7 8 65

Minimum 800 225 689

requirement

.Formulate the LJ>.model for the problem

.Q8) (a) Differentiatebetween PERT& CPM.What is the significanceof 'working

out of float' in network?

(b) A project schedule has the followingchanicteristics:

Q9) (a) Explain in brief the main characteristics of the "Queuing System". Discuss. the fields of application for queuing.

(b) Discuss the various steps of simulation. Distinguish between solutionsderived from simulation models and solutions from analytical models.

.. -"'='"':"-"' "- --:::: ..- - - -

]1.1-506 3

Activity Time Activity Time

1-2 4 5-6 4 .-

1-3 1 5-7 8

2-4 1 6-8 1

3-4 1 7-8 2 -

3-5 6 8-10 5

4-9 5 . 9-10 7

(i) Construct the network diagram.

(ii) Calculate EST, LST, EFT, LFT & slack for each event

(iii) Find out the critical path.