GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VI (OLD) EXAMINATION - WINTER 2018
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Subject Code:161601 Date: 15/12/2018Subject Name: Modelling Simulation And Operations Research
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 State the definition of Operation Research. Also explain the applications of Operation Research. 07
Q.2 A manufacturer produces two types of models M1 and M2. Each model of the type M1 requires 4 hours of grinding and 2 hours of polishing; whereas each model of M2 requires 2 hours of grinding and 5 hours of polishing. The manufacturer has 2 grinders and 3 polishers. Each grinder works for 40 hours a week and each polisher works 60 hours a week. Profit on M1 model is Rs.3.00 and on model M2 is Rs.4.00. Whatever produced in a week is sold in the market. How should the manufacturer allocate his production capacity to the two types of models, so that he makes maximum profit in a week? 07
Q.3 Solve the following LPP by graphical method 07
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Maximize Z = 5X1 + 3X2 Subject to constraints2X1+X2 <1000
X1<400
X1<700 where X1,X2>0
Q.3 Solve following LPP using Simplex Method:
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5X1 + 10X2 + 8X3= Z (Z is the total profit per day) which is to be maximizedConstraints 3X1 +4X2 +5X3 < 60
5X1 +4X2 +4X3< 72
2X1 +4X2 +5X3< 100
X1,X2,X3 =0, Non negativity constraint
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OR
Solve following LPP by Big-M method. 07
60X1 + 80X2 = G (G is the total cost perday which is to be minimized)
Constraints:20X1+30X2 > 900
40X1+30X2 > 1200
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X1,X2 =0 Non-negativity constraintQ.4 (a) Explain primal and dual relationship. 07
(b) Solve blow example using North West Corner rule, the Least Cost method and the Vogel’s Approximation Method of obtaining an initial feasible solution for a transportation problem. 07
Plants Markets Plant capacities
W1 W2 W3
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P1 3 4 2 30P2 2 1 5 25
P3 4 3 3 20
Market 20 20 35
requirements
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OR
A company has three production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below. 07
D1 D2 D3 D4 Supply
S1 19 30 50 10 7
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S2 70 30 40 60 9S3 40 8 70 20 18
Demand 5 8 7 14 34
(a) Formulate this transportation problem as an LP model to minimize the total transportation cost. 07
(b) Consider the following transportation cost table. The costs are given in Rupees, the supply and demand are in units. Determine an optimal solution. 07
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Source 1 2 3 4 5 Supply
1 40 36 26 38 30 160
11 38 28 34 34 198 280
i 36 38 24 28 30 240
Demand 160 160 200 120 240
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Q.4 (a) Explain HAM method in detail 07
(b) Draw a network 07
Activity Immediate Predecessor(s) Activity Immediate Predecessor(s)
A - H F
B - I C,D,GH
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C - J ID - K I
E A L JK
F B M JK
G E N M
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OR
Q.4 (a) Solve the assignment optimal solution using HAM. 07
Time Taken (in minutes) by 4 worker
Job
Worker A B C D
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1 45 40 51 672 57 42 63 55
3 49 52 48 64
4 41 45 60 55
(b) Given the following information on a small project: A is the first activity of the project and precedes the activity B and C. The activity D succeeds both B and C whereas only C is required to start activity E. D precedes F while G succeeds E. H is the last activity of the project and succeeds F and G. Draw a network based on this information. 07
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Q.5 (a) What is queuing theory? Explain operating characteristics of the queuing system. 07
(b) What is Replacement? Explain Group and individual replacement policies giving by example. 07
OR
Q.5 (a) A confectioner sells confectionery items past data of demand per week in 100 kg with frequency is given below. 07
Demand per week 0 5 10 15 20 25
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Frequency 2 11 8 21 5 3Using the following sequence of random number generate the demand for next 15 weeks, also find average demand per week Random : 35,52,90,13,23,73,34,57,83,94,56,67,66,60 07
(b) A TV repairman finds that the time spent on his job has an exponential distribution with mean 30 minutes. If he repairs set in the order in which they come and if the arrival of sets is approximately Poisson with an average rate of 10 per 8-hour day, what is his expected idle time each day? How many jobs are ahead of the set just brought in? 07
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