STUPIDSID
1 (a)
What is Operation Research ? Discuss Importance of Operation Research
in Information and Technology application building.
7 M
1 (b)
A company manufactures 3 types of parts which use precious metals
platinum and gold. Due to shortage of these precious metals, the
government regulates the amount that may be used per day. The relevant
data with respect to supply, requirements and profits are summarized in
the table as follows:
Daily allotment of platinum and gold are 160gm and 120gm respectively. How should company divide the supply of scarce precious metals? Formulate it as a linear programming problem.
| Product | Platinum required unit (gms) | Gold required unit(gms) | Profit/unit (Rs.) |
| A | 2 | 3 | 500 |
| B | 4 | 2 | 600 |
| C | 6 | 4 | 1200 |
Daily allotment of platinum and gold are 160gm and 120gm respectively. How should company divide the supply of scarce precious metals? Formulate it as a linear programming problem.
4 M
1 (c)
Explain the steps followed to solve LPPs by graphical method.
3 M
2 (a)
Solve this LPP problem graphically.
Maximize Z = X 1 + 3X2
Subject to the constraint
X1 + 2X2 ≤ 9
X 1 + 4X2≤ 11
X 1 ? X2≤ 2 and X1 ,X2 ≥ 0.
Maximize Z = X 1 + 3X2
Subject to the constraint
X1 + 2X2 ≤ 9
X 1 + 4X2≤ 11
X 1 ? X2≤ 2 and X1 ,X2 ≥ 0.
7 M
2 (b)
Use simplex method to solve following LPPs
Maximize Z = 7X1 +14X2
Subject to 3X1 + 2X2 <= 36, X1 + 4X2 <=10 X1 >=0 , X2 >=0.
Maximize Z = 7X1 +14X2
Subject to 3X1 + 2X2 <= 36, X1 + 4X2 <=10 X1 >=0 , X2 >=0.
7 M
2 (c)
Explain the concept and computational steps of the simplex method for
solving linear programming problem. How would you identify whether
an optimal solution to a problem obtained using simplex algorithm is
unique or not ?
7 M
3 (a)
Discuss the Northwest and Least cost method for finding initial basic solution. Give its advantage and disadvantage.
7 M
3 (b)
Solve the transportation problem and obtain initial feasible solution calculated by Vogel's Approximation Method
| D1 | D2 | D3 | D4 | D5 | Supply | |
| S1 | 4 | 2 | 3 | 2 | 6 | 8 |
| S2 | 5 | 4 | 5 | 2 | 1 | 12 |
| S3 | 6 | 5 | 4 | 7 | 7 | 10 |
| Demand | 4 | 4 | 6 | 8 | 8 |
7 M
3 (c)
How you deal with the assignment problems where
(a) Some assignment are prohibited ?
(b) The objective function is of maximization type ?
(a) Some assignment are prohibited ?
(b) The objective function is of maximization type ?
7 M
3 (d)
ABC company is engaged in manufacturing 5 brands of packed snacks. It has five manufacturing setup, each capable of manufacturing any of its
brands one at a time, The costs to make a brand on these setups vary
according to following table.
Find the optimum assignment on these setups resulting in the minimum Cost?
| S1 | S2 | S3 | S4 | S5 | |
| B1 | 4 | 6 | 7 | 5 | 11 |
| B2 | 7 | 3 | 6 | 9 | 5 |
| B3 | 8 | 5 | 4 | 6 | 9 |
| B4 | 9 | 12 | 7 | 11 | 0 |
| B5 | 7 | 5 | 9 | 8 | 11 |
Find the optimum assignment on these setups resulting in the minimum Cost?
7 M
4 (a)
What is critical path? State the necessary and sufficient condition of
critical path. Can a project have multiple critical path ?
7 M
4 (b)
Consider the following data for the activity of the project:
Draw the network find the critical path.
| Activity | 1-2 | 1-3 | 1-4 | 2-5 | 3-6 | 3-7 | 4-6 | 5-8 | 6-9 | 7-8 | 8-9 |
| Duration | 2 | 2 | 1 | 4 | 8 | 5 | 3 | 1 | 5 | 4 | 3 |
Draw the network find the critical path.
7 M
4 (c)
Explain following queuing model with example in Information
Technology filed.
(1) First come first served (2) Last come first served (3) Random pick service.
(1) First come first served (2) Last come first served (3) Random pick service.
7 M
4 (d)
At a certain petrol pump, customer arrives in a Poisson process with an
average time of five minutes between successive arrivals. The time taken
at the petrol pump to serve customers follows the exponential distribution
with an average of two minutes. You are required to obtain the following
(a) Arrival and service rate
(b) The utilization parameter
(c) Excepted queue length
(d) Expected number of customer in the system.
(a) Arrival and service rate
(b) The utilization parameter
(c) Excepted queue length
(d) Expected number of customer in the system.
7 M
5 (a)
A firm has a machine whose purchase price is Rs.20,000. Its maintenance
cost and resale price at the end of the different years are as given here:
Obtain the economic life of the machine and the minimum average cost.
| Year | 1 | 2 | 3 | 4 | 5 | 6 |
| Maintenance cost | 1500 | 1700 | 2000 | 2500 | 3500 | 5500 |
| Resale price | 17000 | 15300 | 14000 | 12000 | 8000 | 3000 |
Obtain the economic life of the machine and the minimum average cost.
7 M
5 (b)
What is simulation? Explain the process of simulation.
7 M
5 (c)
Define the simulation model. Distinguish between deterministic and stochastic simulation mode.
7 M
5 (d)
Explain group replacement policy with suitable example.
7 M
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