Hbc 2239: Operation Research Ii Question Paper

Hbc 2239: Operation Research Ii 

Course:Bachelor Of Commerce

Institution: Dedan Kimathi University Of Technology question papers

Exam Year:2014



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DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
University Examination 2013/2014
THIRD YEAR FIRST SEMESTER EXAMINATIONS FOR THE DEGREE OF BACHELOR OF COMMERCE
HBC 2239: OPERATION RESEARCH II
DATE: 22nd April 2014 TIME: 2.00pm – 4.00pm
INSTRUCTIONS: Answer Question One (Compulsory) and any other Two Questions.
QUESTION ONE (COMPULSORY) (30 MARKS)
a) Define the following terms as used in network flows.
(i) A chain
(ii) A path
(iii)An arc (3 marks)
b) Define the following terms as used in Markov chains Analysis.
(i) Communicating states
(ii) Transient state
(iii)Periodic state
(iv) Closed set
(4 marks)
c) Suppose that a new vehicle cost 10000andthattheannualoperationalcostandresalevalueofthevehicleareasshowninthebelow;Ageofvehicle(yrs)Resalevalue()
Operating cost ()17000300(Yr1)26000500(Yr2)34000800(Yr3)430001200(Yr4)520001600(Yr5)610002200(Yr6)Ifyoupurchaseanewvehiclenow,determineareplacementpolicythatminimisesthenetcostofowningandoperatingavehicleforthenextsixyears.(8marks)2|Paged)Considerthethreestatemarkerchainhavingtransitionprobabilitymatrix(i)Drawatransitiongraphofthechain.(2marks)(ii)Isthechainirreducible?Givereasonsforyouranswer.(1mark)(iii)Determinethesteadystatedistributionofthemarkerchain.(6marks)e)Determinethetotaloutputrequiredtosatisfyfinaldemandsof150,260and80forthreeindustriesrespectivelygiventhefollowingmatrixoftechnicalcoefficients.(6marks)QUESTIONTWO(20MARKS)a)AcompanyproducestwotypesofJuices,type1andtype2.Giventhatifapersonlastpurchasedtype1,thereis90 12000
Age of car (yrs)
Annual maintenance cost()Cartradeinprices()
0
2000
7000
1
4000
6000
2
5000
2000
3
9000
1000
4
12000
0
Find the minimum net cost that can be incurred in operating the car during the next five years. (10 marks)
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QUESTION FIVE (20 MARKS)
a) Show that where is the change in the final output vector, is the change in the final demand vector and A is the matrix of technical coefficient. (4marks)
b) Three sectors of economy consist of wood, chair and gum industries i.e W, C and G. The flow of inputs and outputs between the industries is represented in the table below.
INPUTS
Final demand
Outputs (tons)
W
C
G
W
10000
16250
18750
5000
R
15000
32500
18750
15000
G
20000
16250
6250
20000
(i) Obtain the technical coefficient matrix. (2 marks)
(ii) If the final demand for wood sector increases by 600 tons and that of the gum sector falls by 300 tons and the final demand for the chairs remain unchanged, what is the output level for each sector? (7 marks)
c) The following are capacities of water system network.
C(S, 1) = 2 C (2, T) = 3
C (S, 2) =6 C (3, 2)= 2
C (1, T) = 1 C (3, T) = T
C (1, 3) = 2
C (2, 3) = 2
Where S is the source and T is the sink. Sketch the network and find the maximum flow and the corresponding capacity of the minimum cut. (7 marks)






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