STUPIDSID
1 (a)
Write the applications of operation research.
7 M
1 (b)
Write the difference between primal and dual in case of linear programming
problem.
7 M
2 (a)
A factory uses three machines to produce two machine parts. The following table
represents the machining time for each part and other related information. Find
the number of parts to be manufactured per week to maximize the profit.
comments on the obtained solution.
| Machine | Time for machining (min.) |
Max. time available per week Per week |
|
| Part I | Part II | ||
| Lathe | 12 | 6 | 30000 |
| Milling | 4 | 10 | 20000 |
| Grinding | 2 | 3 | 900 |
| Profit/unit (Rs.) | 40 | 100 | |
7 M
Solve any one question from Q2(b) & Q2(c)
2 (b)
The transportation costs incurred to the four factories (P, Q, R & S) and their
capacities are as shown in table. The production costs to them are Rs. 2, 3, 1 and
5 respectively. Whereas, demands of market A, B, C, D are 25, 35, 105, 20
respectively. Propose the deliveries from each of factories to each market so the
total production and transportation cost is the minimum. Use VAM and MODI
Methods.
| A | B | C | D | Capacity | |
| P | 2 | 4 | 6 | 11 | 50 |
| Q | 10 | 8 | 7 | 5 | 70 |
| R | 13 | 3 | 9 | 12 | 30 |
| S | 4 | 6 | 8 | 13 | 50 |
7 M
2 (c)
Solve following LPP by simplex method only and commentss on your special
observations if any.
Maximize Z=2X1+X2.
Subject to constraints:
4X1+3X2≤12,
4X1+X2≤8.
4X1-X2≤8
X1, X2≥0
Maximize Z=2X1+X2.
Subject to constraints:
4X1+3X2≤12,
4X1+X2≤8.
4X1-X2≤8
X1, X2≥0
7 M
Solve any two question from Q3(a), Q3(b) & Q3(c), Q3(d)
3 (a)
The following is the cost matrix of assigning the 4 operators to 4 jobs. Each operator is assigned only one job so as to minimize the total cost of jobs. What
will be the total minimum job cost?
| Operators | Job | |||
| J1 | J2 | J3 | J4 | |
| O1 | 2 | 10 | 9 | 7 |
| O2 | 15 | 4 | 14 | 8 |
| O3 | 13 | 14 | 16 | 11 |
| O4 | 4 | 15 | 13 | 9 |
7 M
3 (b)
Define: Pay off, Value of game, Saddle point.
7 M
3 (c)
Write the canonical form of assignment model and compare with the transportation model.
7 M
3 (d)
From the following survival table, calculate the probability of staff resignation in each year.
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of original staff in service at end of year. | 1000 | 940 | 820 | 580 | 400 | 280 | 190 | 130 | 70 | 30 | 0 |
7 M
Solve any two question from Q4(a), Q4(b) & Q4(c), Q4(d)
4 (a)
Cars arrive at service station every 15 minutes and the service time is 33 minutes.
If the line capacity of service station is limited to 5 cars then find the probability
that the service station is empty and the average number of cars in the system.
7 M
4 (b)
Draw a network for following project;
| Activity | A | B | C | E | F | G | H | I | J | K |
| Predecessor | - | - | - | A | A,B | B,C | C | E,F | G,H | H |
7 M
4 (c)
A company uses fixed order quantity inventory system. The annual demand of
the item is 20000 units. The cost per unit is Rs. 15 and ordering cost is Rs 200
per production run. The holding cost is 22% of cost of unit. Lead time in the past
has been 10, 12, 20, 25, 28 days. Calculate safety stock, reorder level and average
level of inventory.
7 M
4 (d)
Define: Event, Dummy activity, Free float
7 M
Solve any two question from Q5(a), Q5(b) & Q5(c), Q5(d)
5 (a)
Enlist the advantages and limitations of simulation.
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5 (b)
Write the characteristics of dynamic programming.
7 M
5 (c)
Explain steps in Monte Carlo simulation process.
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5 (d)
Explain the Bellman's Principle of optimality with illustrative example.
7 M
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