STUPIDSID
1(a)
What are the scope and limitations odf system Approach?
9 M
Solve any one question fromQ.1(a,b) and Q.2(a,b)
1(b)
Explain with sketch. Global optima and local optima.
6 M
2(a)
Using golden section method, solve the following using 3 iterations Minimize Z=x2-x+2 in the range (0,2)
4 M
2(b)
State any two applications of NLP.
6 M
3(a)
A company has one nob sharpening machine. The nobs required regrinding are sent form the companies tool crib to this machine which at present is operated one shift per day 8 hrs duration. Arrival of the nobs at tool crib is random with an average time of 60 min between one arrival and next. The regarding time of nob is distributed negative exponentially with the mean of 30 min
i) For what fraction of time, the machine is busy?
ii) How does a nob wait in the queue?
iii) What is the average length of queue that is formed from time to time? v) The management has decided to purchase another grinder and thereby start another shift on this machine, when the utilization of machine on single shift basis increases by 85%, what should be the arrival rate then?
i) For what fraction of time, the machine is busy?
ii) How does a nob wait in the queue?
iii) What is the average length of queue that is formed from time to time? v) The management has decided to purchase another grinder and thereby start another shift on this machine, when the utilization of machine on single shift basis increases by 85%, what should be the arrival rate then?
4 M
Solve any one question fromQ.3(a,b) and Q.4(a,b)
3(b)
Explain the process of sequencing of n jobs through 3 machines.
6 M
4(a)
Wriet algorithm for steepest gradient method.
4 M
4(b)
Interarrival and service time in a waiting line problem have the following frequency distribution based on 100 such interations.
Random numbers: 15, 19, 61, 49, 54, 73, 85, 96, 31, 22
Random numbers: 9, 11, 90, 64, 37, 29, 43, 78, 87, 56 Calculate average waiting time and average idle time.
| Interarrival time (min) | 3 | 6 | 9 | 12 | 15 | 18 |
| Frequency | 6 | 9 | 25 | 37 | 16 | 7 |
Random numbers: 15, 19, 61, 49, 54, 73, 85, 96, 31, 22
| Service time (min) | 4 | 6 | 8 | 10 | 12 |
| Frequency | 4 | 10 | 18 | 44 | 24 |
Random numbers: 9, 11, 90, 64, 37, 29, 43, 78, 87, 56 Calculate average waiting time and average idle time.
6 M
Solve any one question fromQ.5(a,b,c) and Q.6(a,b)
5(a)
What is Dynamic programming ? What sort of problems can be solved using it?
5 M
5(b)
Explain Bellman's Principle of optimality.
5 M
5(c)
A distance network consists of eleven nodes which are distributed as shown in following table. Find the shortest path form node 1 to node 11 and the corresponding distance.
| Arc | Distance | Arc | distance |
| 1-2 | 5 | 5-8 | 9 |
| 1-3 | 8 | 5-9 | 6 |
| 1-4 | 3 | 6-9 | 7 |
| 2-5 | 0 | 7-10 | 4 |
| 3-6 | 10 | 8-11 | 6 |
| 3-7 | 12 | 9-11 | 5 |
| 4-7 | 5 | 10-11 | 2 |
6 M
6(a)
What is the need of Dynamic Programming? How is it different from LP? Write some applications of DP.
8 M
6(b)
An organization is planning to diversify its business with a maximum outlay of Rs 4 crores. Out of there identified locations of plant; it can invest in one or more of these plants subject to availability of funds. The different possible alternatives and their investment and present worth of returns (both in crores of rupees) during the usesfull life of each plant is given below.
Find optimum allocation of the capital to different plants which will maximize the corresponding sum of present worth of returns.
| Alternatives | Plant 1 | Plant 2 | Plant 3 | |||
| Cost | Returns | Cost | Returns | Cost | Returns | |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 1 | 12 | 2 | 16 | 2 | 9 |
| 3 | 2 | 15 | 3 | 20 | 3 | 12 |
| 4 | 3 | 19 | 4 | 25 | 4 | 15 |
Find optimum allocation of the capital to different plants which will maximize the corresponding sum of present worth of returns.
8 M
Solve any one question fromQ7(a,b,c) and Q.8(a,b,c)
7(a)
Exlain graphical method of solving Linear programming problem. What are its limitations?
6 M
7(b)
An engineering company is planning to diversify its operations during year 2016-17. The comapny has allocated capital expenditure budget equal to Rs 5.15 crore in year 2016 and Rs 6.5 Crores in year 2017. The company has five investment projects under considerations. The estimated net returns expected cash expenditure are as follows.
Formulate the capital budgeting problem as an LP model to maximize the net returns.
| Project | Estimated net returns(in lakh of Rs) | Capital expenditure (in Lakh of Rs) | |
| Year 2016 | Year 2017 | ||
| A | 12.4 | 2.4 | 3.6 |
| B | 13.9 | 4.5 | 5.7 |
| C | 18.3 | 5.6 | 7.8 |
| D | 24.9 | 7.9 | 8.6 |
| E | 28.9 | 8.5 | 10.2 |
Formulate the capital budgeting problem as an LP model to maximize the net returns.
6 M
7(c)
Solve using simplex method \[\begin{align*} \text{Maximize} Z &= 20X_1+80 X_2\\
\text{Subject to}\ &4X_1+6X_2\leq 90\\
&8X_1+6X_2\leq 100\\
&5X_1+4X_2\leq 80 \\
&X_1,X_2\geq 0\end{align*}\]
6 M
8(a)
Solve by using big M method. \[\begin{align*} \text{Maximize} Z &= 2X_1+3 X_2\\
\text{Subject to}\ &X_1+X_2\geq 6\\
&7X_1+X_2\geq 14\\
&X_1,X_2\geq 0\end{align*}\]
8 M
8(b)
What are the characteristics of Duality?
6 M
8(c)
Construct dual of the primal problem. \[\begin{align*} \text{Maximize} Z &= 3X_1-2 X_2+6X_3\\
\text{Subject to}\ &4X_1+5X_2+4X_3\geq 7\\
&5X_1+X_2+2X_3 \geq 5\\
&7X_1-2X_2-X_3\leq 10\\
&2X_1-X_2+5X_3\geq 6 \\
&4X_1+ 7X_2-X_3\geq 2
\\
&X_1,X_2X_3\geq 0\end{align*}
\]
4 M
Solve any one question fromQ9(a,b,c) and Q.10(a,b,c)
9(a)
Find initial solution of the transportation problem given in Que 10 c) using VAM.
5 M
9(b)
What is degeneracy in transportation problem? How is it resolved?
5 M
9(c)
Following are the details of processing time required for five jobs by five operators. Assign these jobs to operators to give minimum processing time.
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6 M
10(a)
Write short note assignment problem and its applications.
5 M
10(b)
State the steps to handle following situations in assignment problem
i) Maximization
ii) Unbalanced problem
i) Maximization
ii) Unbalanced problem
5 M
10(c)
Solve the following transportation problem to minimize total transportation cost using row maxima and column minima method.
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6 M
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