Model Question Paper - I - Or - 5TH SEM

7/28/2019 Model Question Paper - I - Or - 5TH SEM

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M.S. RAMAIAH INSTITUTE OF TECHNOLOGY, BANGALORE – 54(Autonomous Institute, Affiliated to VTU)

DEPARTMENT OF INDUSTRIAL ENGINEERING AND MANAGEMENT

MODEL QUESTION PAPER – 1

OPERATIONS RESEARCH – IM504Time: 3 hrs Max.

Marks: 100

NOTE: 1) PART A is Compulsory2) PART B Answer five full questions choosing one from

each unit

PART – A

1) The mathematical technique for finding the best use of limited resourcesin an optimum

manner is known as

(a) Operations Research (b) Linear Programming (c) Network Analysis (d)Queuing Theory

2) A linear programming problem is called so, because in that problem(a) all the functions expressing the constraints are linear (b) the

objective functionshould also be linear (c) both (a) & (b) above (d) none of the

above.

3) Linear programming can be applied to(a) steel industry (b) oil industry (c) chemical industry (d) all of the above

4) In the graphical method of linear programming problem, every corner of the feasible polygon

indicates(a)a basic feasible solution (b) optimum solution (c) both (a) & (b) above(d) none of the above.

5) In canonical form of linear programming model(a) all the inequalities indicating the constraints are in the same manner

(b) the right-handside of the inequation are constraints (c) all the variables are non-

negative(d) all of the above

6) The simplex method is the basic method for(a) value analysis (b) operations research (c) linear programming (d)

model analysis

7) In the simplex method, the variables which have not been assigned thevalue zero, during an

iteration, are called as



(a)basic variable (b) artificial variable (c) slack variable (d) none of theabove.

8) A basic feasible solution in simplex method is one, when(a) all the decision variables are in the base (b) all the decision variables

and surplus variablesare assigned zero values (c) all the base variables are non – negative (d)

all the base variables

satisfy the constraint equations.

9) Graphical method, simplex method and transportation method areconcerned with

(a) value analysis (b) linear programming (c) break-even analysis (d)queuing theory

2

10) Artificial variable is introduced in the simplex method to(a) determine the IBFS, when surplus variable is present (b) convert the

inequation with the

sign greater than or equal to, in the form of an equation (c) apply Big- Mmethod for

solution to LPP (d) indicate the sensitivity of surplus variable.

11) Dual of the dual is the(a) dual (b) primal (c) either dual or primal (d) none of the above

12) At the optimum level (i.e., final iteration) the values of the slack variablesin the primals are

(a) positive (b) negative (c) zero (d) none of the above

13) In transportation problem, during an iteration, the total no. of allocationshould not be

more than(a)m + n (b) m + n + 1 (c) m + n – 1 (d) m – n – 1

14) The IBFS can be determined by the application of (a) northwest corner method (b) least cost method (c) vogel’s

approximation method(d) all the above

15) Optimality is reached when all the index values are(a) zero (b) negative (c) positive (d) none of the above

16) In assignment model(a) degeneracy always present in all the problems (b) no. of resources is

equal to no. of jobs(c) only one unit of the ith source can be assigned to any one of its

destinations(d) all the above



17) In an n x n matrix of an assignment problem, the optimality is reachedwhen the minimum

number of straight lines scoring all the zeros is(a)n2 (b) 1 / n (c) n (d) none of the above

18) In pert network, some times dummy activities are introduced to(a) prevent cycling of network (b) maintain network logic of precedence

(c) avoid crossing of

activities in the network (d) have an activity with zero duration of time

19) A pert activity has an optimistic tie of 3 days, pessimistic time of 15 daysand the expected

time is 7 days. The most likely time of the activity is(a)5 days (b) 6 days (c) 7 days (d) 9 days

20) The estimated duration of times for an activity, in the PERT networkunder the worst and

best environment are 9 days and 3 days. The variance of this activity is(a)6 days (b) 1 day (c) 2 days (d) none of the above

21) In a M/M/1 Queue, the service rate is(a) poisson (b) exponential (c) linear (d) none of the above

3

22) M/M/1 model is(a) a single channel & single service unit (b) a “First come, First serve

basis”(c) a system having probability distribution independent of time (d) all of

the above

23) Queue length (Lq) is equal to

(a)ς

ς

−1(b)

ς

ς

−1

2

(c) )1(

1

ς

ς

λ −

(d) )1(

1

ς

ς

− M

24) A situation is termed as competitive situation when(a) the action of one depends on the action of the other (b) the action of

one does notdepend on the action of the other (c) the action of one does not follow

any logic(d) none of the above

25) A pay-off, which is an outcome of all combination of courses of action is(a) positive (b) negative (c) zero (d) all of the above

PART – B

UNIT – I

1 a) What is OR? Describe briefly its applications.5



b) The manager of an oil refinery has to decide upon the optimal mix of 2possible blending

processes of which the inputs and outputs per production run are asfollows 10

Input OutputProcess Crude A Crude B Gasoline X Gasoline Y

1 5 3 5 82 4 5 4 4

The maximum amounts available of Crude A & B are 200 units and 150units

respectively. Market requirements shows that at least 100 units of gasoline X and 80

units of gasoline must be produced. Profits per production run fromprocess 1 & process

2 are Rs.30 & Rs.40 respectively. Formulate the LPP & solve itgraphically.

2 a) List and explain the important phases of OR study.6

b) Solve the following LPP graphically9

Maximize Z = 2x1 + x2

Subject to x2 ≤ 102x1 + x2 ≤ 60

x1 + x2 ≤ 183x1 + x2 ≤ 44x1, x2 ≥ 0

4

UNIT – II

3) Solve the following LPP by Simplex method15

Maximize Z = 5x1 + 2x2 + 10x3

Subject to x1 – x3 ≤ 10x2 – 3x3 ≥ 10x1 + x2 + x3 ≤ 10

x1, x2, x3 ≥ 0

4) Solve the following LPP by using the dual simplex method15

Maximize Z = 6x1 + 7x2 + 3x3 + 5x4

Subject to 5x1 + 6x2 – 3x3 + 4x4 ≥ 12x2 + 5x3 - 6x4 ≥ 102x1 + 5x2 + x3 + x4 ≥ 8

x1, x2, x3, x4 ≥ 0



UNIT – III

5 a) What are the rules to determine degeneracy?3

b) Freshwater is supplied through 3 reservoirs with daily supply capacities of 15,20 & 25 million ltrs

of water respectively. On each day supply must be provided for 4 cities A, B, C& D whose demands

are 8, 10, 12 & 15 million litres respectively whose costs are given below:12

Cities

A B C D1 2 3 4 5

Reservoirs 2 3 2 5 2

3 4 1 5 2

Use the transportation algorithm to determine the cheapest pumping

schedule, if excesswater can be disposed of at no cost.

6) A firm produces a component and distributes them to 5 wholesalers at afixed price of Rs.

10/unit. Sales forecast indicate that monthly demand will be 3,000, 3,000,1,000, 5,000 and 4,000 units at wholesale dealers a, b, c, d & e

respectively. The monthlyproduction capacities are 5,000, 1,000 & 10,000 at plants A, B & C

respectively. Theproduction costs are Rs. 2, Rs. 1 & Rs. 3 at plants A, B & C respectively.

The unittransportation cost in rupees between the plants and wholesalers are

given in the followingtable

15

WholesalesPlants a b c d e

A 0.5 0.5 1.0 1.5 1.5B 1.0 0.5 1.0 1.0 1.5

C 1.0 1.0 0.5 1.5 1.0Determine the transportation schedule between plants and wholesalers

in order tomaximize the total profit per month. Use VAM to obtain the IBFS.

5

UNIT – IV

7 a) The owner of a machine shop has 4 machinists available to assign to jobs for that day. Five



jobs are offered with expected profit for each machinist on each job asfollows 9

A B C D E

1 60 76 48 99 802 69 82 59 71 573 85 90 109 69 79

4 46 62 85 75 78

Determine the optimum assignment schedule. Which job should bedeclined?b) The following table gives the activities of a construction project and otherrelevant

information10

Activity 1 – 2 1 – 3 2 – 3 2 – 4 3 – 4 4 – 5

Duration 20 25 10 12 6 10

(i) Draw the network for the project (ii) Find critical path

8) The following table lists the jobs of a network along with their timeestimates 15

Duration in days Jobs

Optimistic Most likely Pessimistic

1 – 2 3 6 152 – 3 6 12 302 – 4 5 11 173 – 4 3 9 273 – 5 1 4 75 – 6 2 5 83 – 6 4 19 284 – 6 2 5 14

(i) Draw the network and calculate the length and variance of criticalpath

(ii) What is the probability that jobs on critical path will be completedby the due date of 40 days?

(iii) What is your estimate of the probability that the entire project willbe completed by the due date?



6

UNIT – V

9 a) Explain Kendal – lee notation for M/M/1 Model3

b) The arrival of customers at a banking counter follows poissondistribution with a mean of

45 per hour12

(i) What is the probability of having zero customer in the system (Po)?(ii) What is the probability of having 5 customers in the system?

Probability of having 10customers in the system.

(iii) Determine the steady state performance statistics, namely, Ls, Lq, Ws

& Wq?

10 a) Define the following

3 (a) Saddle Point (b) Fair gameb) The following matrix represents the payoff to P1 in a rectangular game

between twopersons P1 & P2

12

8 15 - 4 - 219 15 17 160 20 15 5

By the notion of dominance, reduce the game to 2 x 4 game & thensolve it graphically.

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Model Question Paper - I - Or - 5TH SEM