MCIS Operation Research Questions

Pokhara University
Semester-Fall
Level: Master 
Year: 2016
Program: MCIS
Full Mark: 100
Course: Operation research   
Pass Mark: 60
Time: 4 hrs 
 

Candidates are required to given their answers in their own words as far as practicable.

1

Formulate and solve it bye graphical method. (10)

2. Wild West produces two types of cowboy hats.

Formulate the problem as an LPP so as to maximize the profit and solve by simplex method. (10)

3.Write the dual of the primal (5)
Max Z=2×1+3×2+4×3
Subject to constraints
X1-5×2+3×3=7
2×1-5×2 <=3 3×2-5×3>=5
X1,x2>=0 and x3 is unrestricted in sign.

4. A company has received a contract to supply gravel for three new construction projects located in town A, B and C. Construction engineers have estimated the required amounts of gravel which will be needed at these construction project:

Project locationWeekly requirement (truckloads)
A72
B102
C41

The company has 3gravel pits located in town X, Y, Z.

The amount of gravel which can be supplied by each pit is as follows:

plantXYZ
Amount available (truckloads)768277

The company has computed the delivery cost from each pit to each project site. These costs (Rs.) are shown in following table:

Project location

ABC
488
162416
81624

Also find minimum cost with optimality. (15)

5 .In the modification of a plant layout of a factory, four new machine M1,M2,M3, M4 are to be installed in a machine shop. There are five vacant places A,B,C,D, E available. Because of limited space machine M2 can’t be placed at C and M3 can’t be placed at A. The cost of locating a machine at place( in hundred rupees) as follows:

 ABCDE
M1911151011
M2129109
M31114117
M448278

Find optimal assignment schedule. (5)

6. Use the algorithm of Dijkstra to find the shortest route in the network between node 1 and any other node. (10)

7. A project consisting of 6 independent activities is to be analyzed by using PERT. The following information is given. (10)

ActivityABCDEF
Predecessor activityAB,CDA
Optimistic time321012
Pessimistic time52514310
Most likely time423429

i.Draw the diagram of the network, and show the critical path.
ii.What is expect time to complete project?
iii.What is the probability that project will be completed in 20 weeks or less

8. Maximize z=2×1+x2
Subject to constraints
X1+x2<=6 ‘

X1+2×2<=10

X1,x2>0 solve the following LPP by matrix method in revised simplex algorithm (10)

9.Solve the following all-integer linear programming problem by branch and bound method.
Max Z=3×1+5×2
subject to constraints
2×1+4×2<=25
X1<=8
2×2<=10
X1 and x1 are non negative integer.

Or

What is dynamic programming? solve the bounding problem by recursive method of dynamic programming.

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