STUPIDSID
1 (a)
State the general rules for formulating a dual LP problem fro it's primal.
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1 (b)
Nachiketa corporation manufactures two products A1&A2.The profit per unit of the two products is Rs.50& Rs.60 respectively. Both the products require processing in three machines. Below table indicates the available machine hours per week & time require on each machine for one unit of A1 &A2.Formulate as linear programming problem.
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2 (a)
Explain significance of any two assumptions of LPP.
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Answer any two question from Q2 (b) or Q2 (c)
2 (b)
Use graphical method to solve the following LPP.
Maximum Z=17X1+15X2
Subject to:
15X1+25X2≤375
24X1+11X2≤265
All X1, X2 ≥ 0.
Maximum Z=17X1+15X2
Subject to:
15X1+25X2≤375
24X1+11X2≤265
All X1, X2 ≥ 0.
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2 (c)
Solve the following game whose payoff matrix is given below:
| Player B | |||
| Player A | I | π | |
| I | 1 | 8 | |
| π | 6 | 2 |
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Answer any two question from Q3 (a), (b) or Q3 (c), (d)
3 (a)
Distinguish between transportation & transhipment problems in detail.
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3 (b)
Company has factories A1, A2, A3 which supply to warehouses at W1, W2 & W3 Weekly factory capacities are 240, 200 & 130 units respectively. Weekly
Warehouse requirements are 190, 150 & 110 units respectively, Unit transportion in costs Rs. As follows: Find I.B.S. BY VAM method& Optimum solution BY MODI method.
Warehouse requirements are 190, 150 & 110 units respectively, Unit transportion in costs Rs. As follows: Find I.B.S. BY VAM method& Optimum solution BY MODI method.
| W1 | W2 | W3 | SUPPLY | |
| A1 | 16 | 20 | 12 | 240 |
| A2 | 14 | 8 | 18 | 200 |
| A3 | 26 | 24 | 16 | 130 |
| DEMAND | 190 | 150 | 110 | 450 |
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3 (c)
Give different practical applications of transportation problem.
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3 (d)
Obtain an I.B.F.S. to the following transportation problem using N-W Corner method.& Optimum solution BY STEPPING STONE method.
| Q1 | Q2 | Q3 | Q4 | SUPPLY | |
| P1 | 1 | 3 | 2 | 4 | 8 |
| P2 | 5 | 4 | 2 | 0 | 10 |
| P3 | 0 | 3 | 3 | 1 | 12 |
| DEMAND | 4 | 5 | 8 | 5 | 450 |
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Answer any two question from Q4 (a), (b) or Q4 (c), (d)
4 (a)
The production department for a company requires 3500kg.of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs.35& the cost of carrying inventory is 25 percentage of the investment in the inventories. The price is Rs.10 per kg. The purchase manager wishes to determine an ordering policy for raw material.
Calculate
(1)The optimal lot size
(2)The minimum yearly variable inventory cost
(3)The optimal order cycle time
(4)The minimum yearly total inventory cost.
Calculate
(1)The optimal lot size
(2)The minimum yearly variable inventory cost
(3)The optimal order cycle time
(4)The minimum yearly total inventory cost.
7 M
4 (b)
Solve the following assignment problem by minimization method.
| I | II | III | IV | V | |
| M1 | 12 | 5 | 9 | 18 | 11 |
| M2 | 13 | 7 | 6 | 12 | 14 |
| M3 | 3 | 2 | 3 | 4 | 5 |
| M4 | 18 | 9 | 12 | 16 | 15 |
| M5 | 12 | 6 | 14 | 19 | 10 |
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4 (c)
A Project is represented by the Network shown below & has the following data.
Determine
(1)Expected Time &Variance
(2) Earliest & Latest times to reach each event.
(3) The critical path
Determine
(1)Expected Time &Variance
(2) Earliest & Latest times to reach each event.
(3) The critical path
| Task | A | B | C | D | E | F | G | H | I |
| Optimistic time | 5 | 18 | 26 | 16 | 15 | 6 | 7 | 7 | 3 |
| Pessimistic time | 10 | 22 | 40 | 20 | 25 | 12 | 12 | 9 | 5 |
| Most likely time | 8 | 20 | 33 | 18 | 20 | 9 | 10 | 8 | 4 |
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4 (d)
On an average 95 patients per 24 hrs.day require the service of an emergency clinic. Also on the average, a patient requires 12 minutes of an active attention. Assume that the facility can handle only one emergency at a time.Suppoce that it cost the clinic Rs.100 per patient treated to obtain an average servicing of 10 minutes & that minute of decreasing in this average time would cost Rs. 10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from one to one third patients to half a patient.
7 M
Answer any two question from Q5 (a), (b) or Q5 (c), (d)
5 (a)
What is dynamic programming? Discuss the similarities between dynamic & linear programming. How it differs from linear programming?
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5 (b)
A firm is considering replacement of a machine whose cost price is Rs.12200& the scrap value Rs.200.The running costs are found from experience to be as follows. When should the machine be replaced?
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Running Cost Rs. | 200 | 600 | 700 | 1000 | 1200 | 1800 | 2500 | 400 |
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5 (c)
Explain steps in Monte Carlo simulation process.
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5 (d)
Explain definition & scope of operation research.
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