STUPIDSID
1(a)
Operations Research is the art of giving bad answers to the problems which otherwise would have been worst. Justify this statement. Also discuss the scope of Operations Research.
7 M
1(b)
Write the dual of
i) Maximize Subject to
Z= 3X1 + 2X2
X1+X ≥ 1
X1≤ 7
X1+2X2 ≤ 10
X2 ≤ 3
X1, X2 ≥ 0
ii) Maximize Subject To Z=5X1-6X2+4X3
3X1+4X2+6X3≥ 9
X1+3X2+2X3≥ 5
-7X1+2X2+X3 ≥ -10
X1-2X2+4X3 ≥ 4
X1, X2, X3 ≥ 0
i) Maximize Subject to
Z= 3X1 + 2X2
X1+X ≥ 1
X1≤ 7
X1+2X2 ≤ 10
X2 ≤ 3
X1, X2 ≥ 0
ii) Maximize Subject To Z=5X1-6X2+4X3
3X1+4X2+6X3≥ 9
X1+3X2+2X3≥ 5
-7X1+2X2+X3 ≥ -10
X1-2X2+4X3 ≥ 4
X1, X2, X3 ≥ 0
7 M
2(a)
Solve by simplex method
Maximize Subject To
Z=100X1+50X2+50X3
4X1+3X2+2X3 ≤ 100
3X1+8X2+X3≤ 800
4X1+2X2+X3 ≤ 600
X1, X2, X3 ≥ 0
Maximize Subject To
Z=100X1+50X2+50X3
4X1+3X2+2X3 ≤ 100
3X1+8X2+X3≤ 800
4X1+2X2+X3 ≤ 600
X1, X2, X3 ≥ 0
7 M
Solve any one question from Q.2(b) & Q.2(c)
2(b)
A company has to appoint grade A and grade B types of inspectors in the QC dept. Grade A inspector can check 40 pieces /hour with 95 % accuracy, while Grade B inspector can check 30 pieces /hour with 98 % accuracy. At least 4500 pieces are required to be checked in an 8 hour shift per day. Inspectors of Grade A and Grade B are paid Rs 100 and Rs 120 per hour respectively. An error made by inspector cost Rs 15/per error to the company. Formulate the problem of
assigning inspectors to minimize the overall cost per day considering that 20 grade A and 30 grade B inspectors are available to undertake inspection.
7 M
2(c)
What are the advantages and limitations of graphical method in solving LPP? Obtain the solution graphically for the following LPP
Maximize Subject To
Z=3X14X2
5X1+4X2 ≤ 200
3X1+5X2 ≤ 150
5X1+4X2 ≥ 100
8X1+4X2 ≥ 80
X1, X2 ≥ 0
Maximize Subject To
Z=3X14X2
5X1+4X2 ≤ 200
3X1+5X2 ≤ 150
5X1+4X2 ≥ 100
8X1+4X2 ≥ 80
X1, X2 ≥ 0
7 M
Solve any one question from Q.3 & Q.4
3(a)
There are 1000 bulbs installed in a complex. It cost Rs 3/bulb for individual replacement and Rs 0.7/bulb if replaced in group. It has been decided to go for the group replacement of the bulbs (policy being replacing all bulbs at decided
period as well as individual replacement of bulbs failing in this period). The table below gives the mortality rate for the bulb at the end of each month
Find the best interval period for group replacement.
| End of month | 1 | 2 | 3 | 4 | 5 | 6 |
|
Cumulative Probability of failure to date |
0.09 | 0.25 | 0.49 | 0.85 | 0.97 | 1.0 |
Find the best interval period for group replacement.
7 M
3(b)
Discuss Travelling Salesman problem in brief.
The matrix below shows the cost in rupees of processing 3 jobs X, Y and Z on machines A, B and C.
If all jobs can be processed on all machines, assign the jobs to the machines and find the minimum total cost of processing.
The matrix below shows the cost in rupees of processing 3 jobs X, Y and Z on machines A, B and C.
| Machine | ||||
| Job | A | B | C | |
| X | 35 | 25 | 32 | |
| Y | 41 | 30 | 29 | |
| Z | 45 | 34 | 27 | |
If all jobs can be processed on all machines, assign the jobs to the machines and find the minimum total cost of processing.
7 M
4(a)
What is the need for Replacement of any machine?
A machine was purchased with initial investment of Rs 40000. The following is the data available
What will be the expected life as per optimum replacement policy and the average annual cost during this period?
A machine was purchased with initial investment of Rs 40000. The following is the data available
| Year | 1 | 2 | 3 | 4 | 5 | 6 |
|
Operating & Maintenance cost per year in Rs |
1400 | 1450 | 1510 | 1600 | 1720 | 1900 |
|
Salvage Value in Rs |
35000 | 34000 | 32500 | 30500 | 28000 | 25000 |
What will be the expected life as per optimum replacement policy and the average annual cost during this period?
7 M
4(b)
Following is the data collected by the company for one of the item having annual demand of 1000 units:
Interest on the capital locked for inventory = 15%, pilferage of inventory=5% of total inventory cost, other holding cost= 20% of inventory cost, order processing cost/order= Rs 150, order follow up cost/order= Rs 125, inspection and other procurement cost/order= Rs 125.
If the cost per item is Rs 10 and discount offered is 10% for minimum order quantity of 500 items, Should the order be placed without discount for EOQ or with discount for quantity of 500 items? What will be saving by selected option?
Interest on the capital locked for inventory = 15%, pilferage of inventory=5% of total inventory cost, other holding cost= 20% of inventory cost, order processing cost/order= Rs 150, order follow up cost/order= Rs 125, inspection and other procurement cost/order= Rs 125.
If the cost per item is Rs 10 and discount offered is 10% for minimum order quantity of 500 items, Should the order be placed without discount for EOQ or with discount for quantity of 500 items? What will be saving by selected option?
7 M
Solve any one question from Q.5 & Q.6
5(a)
The following is the pay off matrix between player X and player Y. Find the optimal strategies, their frequencies and the value of the game. Use rule of dominance and oddment in calculations
| Player Y | |||||
| A | B | C | D | ||
| Player X | I | 0.25 | 0.20 | 0.14 | 0.30 |
| II | 0.27 | 0.16 | 0.12 | 0.14 | |
| III | 0.35 | 0.08 | 0.15 | 0.19 | |
| IV | -0.02 | 0.08 | 0.13 | 0.00 | |
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5(b)
i) From the simplex table how will you identify the cases of infeasible solution, unbound solution and alternate optimal solutions?
ii) Differentiate between PERT and CPM.
iii) What is a two person zero sum game?
ii) Differentiate between PERT and CPM.
iii) What is a two person zero sum game?
7 M
6(a)
When is dummy required in transportation problem?
Find the basic feasible solution and its cost by i) northwest corner method, ii) Least cost method and iii) Vogel's approximation method for the following transportation table which shows cost in rupees for transporting 1 unit from factories to warehouses
Find the basic feasible solution and its cost by i) northwest corner method, ii) Least cost method and iii) Vogel's approximation method for the following transportation table which shows cost in rupees for transporting 1 unit from factories to warehouses
|
Warehouses |
Supply | |||||
| A | B | C | D | |||
| Factories | X | 2 | 3 | 11 | 7 | 6 |
| Y | 1 | 0 | 6 | 1 | 1 | |
| Z | 5 | 8 | 15 | 9 | 10 | |
| Requirement | 7 | 5 | 3 | 2 | ||
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6(b)
Derive the equation for economic order quantity and total inventory cost for the
classical EOQ model, where demand rate (r) is uniform replenishment rate (d) is
instantaneous. C1 is the Holding cost Rs/unit/unit time, C2 is the order cost in Rs/order.
7 M
Solve any one question from Q.7 & Q.8
7(a)
The following table gives the duration in days and the predecessor for the various
Tasks.
Draw the EON diagram and find the minimum time for completion of the project. Also find the total float for each activity.
| Task | A | B | C | D | E | F | G | H | I |
| Time | 8 | 10 | 8 | 10 | 16 | 17 | 18 | 14 | 9 |
| predecessor | - | - | - | A | A | B, D | C | C | E, G |
Draw the EON diagram and find the minimum time for completion of the project. Also find the total float for each activity.
7 M
7(b)
Define Simulation, explain methodology of simulation in brief and give its advantages and disadvantages.
7 M
8(a)
Explain the terms w.r.t. queuing theory i) Balking ii) Reneging iii) Jockeying At a reservation counter, 20 customers arrive on average every 10 minutes. The
clerk can serve 22 customers in 10 minutes. Find i) average number of customers in the system ,ii) average queue length and iii) average time a customer waits before being served. State assumption made for the probability distribution.
7 M
8(b)
What is dynamic programming? How dynamic programming differs from the routine linear programming? Is solution of LPP possible by dynamic
programming? If yes, How?
7 M
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