Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech Chemical Engineering OPERATION RESEARCH - Question Paper

Model Question Paper

BTAE5/BTBT5/BTCH5/BTC5/BTMR5/BTM5 OPERATION RESEARCH

 

Time : 3 Hrs Maximum Marks : 75

Instructions :

1.Question paper is divided into group A,B and C.

2.Each group is of 25 marks.

3.Figure to the right in bracket indicate marks.

4.Handwriting should be neat and eligible.

 

Group A (25 Marks)

 

Answer any Three Questions(Question 1 is compulsory)

 

Q.1 Determine an initial basic feasible solution to the following transportation

problem by using Vogels Approximation Method. (5)

Destination

D₁ D₂ D₃ D₄ Supply

 

S₁ 21 16 15 3 11

 

Source S₂ 17 18 14 23 13

 

 

S₃ 32 27 18 41 19

 

Demand 6 10 12 15

 

Q.2 Use the simplex method to solve the following LP problem. (10)

Maximize Z = 3x₁ + 5x₂ + 4x₃

Subject to.

2x₁ + 3x₂ 8

2x₂ + 5x₃ 10

3x₁ + 2x₂ + 4x₃ 15

x₁,x₂,x₃ 0.

Q.3 A company is spending Rs.1000 on transportation of its units from three plants to

four distribution centers. The availabilities and requirements of units with unit

cost of transportation are, (10)

 

 

 

 

Distribution centers

D₁ D₂ D₃ D₄ Availabilities

 

P₁ 19 30 50 12 7

Plants P₂ 70 30 40 60 10

 

P₃ 40 10 60 20 18

 

Requirements 5 8 7 15

What can be the maximum saving by optimum distribution?

Q.4 (a) An assembly is to be made from two parts X and Y,Both parts must be

turned on a lathe and Y must be polished whereas X need not be polished

The sequence of activities together with their predecessors is given below:

 

Activity Description Predecessor activity

 

A Open work order ------

B Get material for X A

C Get material for Y A

D Turn X on lathe B

E Turn Y on lathe B,C

F Polish Y E

G Assemble X & Y D,F

H Pack G

Draw a network diagram for the project.

 

(b)    Customers arrive at a booking office window,being manned by a single

individual at rate of 25 per hour. Time required to serve a customer has

exponential distribution with a mean of 120 seconds.Find the mean waiting

time of a customer in the queue. (5)

Q.5 Find the optimal order quantity for a product for which the price discounts are as

follows: (10)

Order Quantity Unit price (Rs.)

 

0 Q < 500 10.00

500 Q < 750 9.25

750 Q 8.75

The monthly demand for the product is 200 units,storage cost is 2% of unit cost

and cost of ordering is Rs.100.

 

 

Group B (25 marks)

 

Answer anyThree Questions (Question 6 is compulsory)

 

Q.6 Discuss the advantages of linear programming . (5)

Q.7 Solve by Graphically, (10)

Maximize Z = 50x₁ + 80x₂

Subject to.

x₁ 80

x₂ 60

5x₁ + 6x₂ 600

x₁ + 2x₂ 160

x₁,x₂ 0.

 

Q.8 Five workers are available to work with the machines and the respective cost

(in Rs) associated with each worker,machine assignment is given below.A sixth

machine is available to replace one of the existing machines and the associated

costs are also given below. (10)

Machine

 

M₁ M₂ M₃ M₄ M₅ M₆

Workers

W₁ 12 3 6 - 5 9

 

W₂ 4 11 - 5 - 3

 

W₃ 8 2 10 9 7 5

 

W₄ - 7 8 6 12 10

 

W₅ 5 8 9 4 6 -

 

(a)    Determine ,whether the new machine can be accepted?

(b)   Determine also optimal assignments and associated saving in cost.

 

 

 

 

 

 

 

Q.9 Obtain the critical path and project duration for the following PERT network.

(10)

6 4

8

10 2 12 10 5 10

9 5

7

 

 

 

Q.10 If for a period of 2 hours in a day, trains arrive at the yard every 20 minutes but

the service time continues to remain 36 minutes, then calculate for this period.

(10)

(a)    The probability that the yard is empty.

(b)   Average line length with the assumption that the line capacity of the yard

Is limited to 4 trains only.

 

 

Group C (25 marks)

All questions are compulsory.

Q.11 (A) Fill in the blanks(Each question carries 2 marks ,Total = 10 marks)

(1)   A feasible solution to a linear programming, which is also basic solution, is

called a ---------------

(2)   The dual of the dual of a primal problem is --------------

(3)   PERT is ---------oriented.

(4)   An activity which must be completed before one or more activities start is

Known as --------------activity.

(5)   The cost of slack and surplus variable is ------------------

 

Q.11 (B) Choose the best answer(Each question carries 2 marks,Tota =10marks)

 

(1)   A basic solution to the system of equations is called -------------- if one or

more the basic variables I become equal to zero.

(a) degenerate (b) solution (c) basic solution (d) optimum

(2)   The value of objective function is -------------for primal and dual problem.

(a) different (b) equal (c) zero (d)none of these

(3)   Expansion of CPM is --------------

(a) critical path method (b) clear path method

(c) critical poisson method (d) none of these.

(4)   The most optimistic time means -------------

(a) longest time (b) shortest time (c) equal time (d) none of these.

(5)   All decision variables are----------------

(a) non- linear (b)discontinuous (c) linear (d) none of these.

Q.11 (C) True or false(Each question carries 1 mark,Total = 5 marks)

 

(1)   The cost of Artificial variable is 1.

(2)   CPM is concerned with time and cost.

(3)   The number of primal decision variables equals the number of dual variables.

(4)   An initial basic feasible solution should consists exactly (m-n + 1)allocations for the transprtation.

(5) CPM is activity oriented.