Exam Details
| Subject | Product Development And Design | |
| Paper | ||
| Exam / Course | Diploma in Mechanical Engineering (DMEVI)& B.Tech. MECHANICAL ENGINEERING 1-4 (BTMEVI) | |
| Department | School of Engineering & Technology (SOET) | |
| Organization | indira gandhi national open university | |
| Position | ||
| Exam Date | June, 2016 | |
| City, State | new delhi, |
Question Paper
No. of Printed Pages: 4 IBIMEE-0041
B.Tech. -VIEP -MECHANICAL ENGINEERING
(BTMEVI)
Term-End Examination June, 2016 ........:-_"
BIMEE-004 OPTIMIZATION TECHNIQUES IN
ENGINEERING
Time hours Maximum Marks: 70 Note: Answer any five questions. All questions carry equal marks. Use of scientific calculator is permitted.
1. What is decision-making Explain and differentiate this under the conditions of certainty and uncertainty.
A company produces two products and and has a total production capacity of 9 units per day, and both requiring the same production capacity. The company has a permanent contract with another company to supply 2 units of and at least 3 units of per day. Each unit of requires 20 machine hours production time and each unit of requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The company makes a profit of Rs 800 per unit of and Rs 1,200 per unit of Determine the production schedule for maximum profit. 7 7
2. In a game of matching coins with two players, suppose A wins one unit of value when there are two heads, wins nothing when there are two tails, and loses 1/2 unit of value when there are one head and one tail. Determine the pay-off matrix, the best strategies for each player and the value of the game to A.
State the necessary and sufficient conditions for the maximum of a multi-variable function. 7 7
3. Explain the methods used in solving integer programming problems.
Solve the following using Kuhn-Tucker conditions:
Maximize z 2x1 -6x2
subject to:
-x1 x2 0
x1^2 x2^2 4
x1, x2 0 7 7
4. Solve the following equations by Jacobi's iteration method:
20x y -2z 17
3x 20y -18
2x 3y 20z 25
By using Modified Euler's method, determine the value of y when
x 0.1 given that:
y(0) and dy/dx x^2 y.
(Take h =0.05) 7 7
5. Apply Runge-Kutta method to find an approximate value of y for x 0.2 in steps of
0.1 if dy/dx y^2 ,
given that:
y 1 when x 0.
Evaluate Integral(1 dx, using Simpson's 1/3 rd rule. The upper and lower limits are 6 and 0 7 7
6. A production control superintendent finds the following information on his desk. In departments B and C the number of surplus pallets is 18, 27 and 21 respectively. In departments I and the number of pallets required is 14, 12, 23 and 17 respectively. The time in minutes to move a pallet from one department to another is given below:
To/From G H I J
A 13 25 12 21
B 18 23 14 9
C 23 15 12 16
What is the optimal distribution plan to minimize the moving time?
Solve the following linear programming problem:
Maximize z 2x1 x2
subject to:
x1 2x2 10
x1 x2 6
x1 -x2 2
x1 2X2 1
x1, x2 0 7 7
7. What is the need of dynamic programming and how is it different from linear programming? State some applications of dynamic programming. List down the advantages,
(ii) the applications, and
(iii) the limitations of simulation. 7 7
B.Tech. -VIEP -MECHANICAL ENGINEERING
(BTMEVI)
Term-End Examination June, 2016 ........:-_"
BIMEE-004 OPTIMIZATION TECHNIQUES IN
ENGINEERING
Time hours Maximum Marks: 70 Note: Answer any five questions. All questions carry equal marks. Use of scientific calculator is permitted.
1. What is decision-making Explain and differentiate this under the conditions of certainty and uncertainty.
A company produces two products and and has a total production capacity of 9 units per day, and both requiring the same production capacity. The company has a permanent contract with another company to supply 2 units of and at least 3 units of per day. Each unit of requires 20 machine hours production time and each unit of requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The company makes a profit of Rs 800 per unit of and Rs 1,200 per unit of Determine the production schedule for maximum profit. 7 7
2. In a game of matching coins with two players, suppose A wins one unit of value when there are two heads, wins nothing when there are two tails, and loses 1/2 unit of value when there are one head and one tail. Determine the pay-off matrix, the best strategies for each player and the value of the game to A.
State the necessary and sufficient conditions for the maximum of a multi-variable function. 7 7
3. Explain the methods used in solving integer programming problems.
Solve the following using Kuhn-Tucker conditions:
Maximize z 2x1 -6x2
subject to:
-x1 x2 0
x1^2 x2^2 4
x1, x2 0 7 7
4. Solve the following equations by Jacobi's iteration method:
20x y -2z 17
3x 20y -18
2x 3y 20z 25
By using Modified Euler's method, determine the value of y when
x 0.1 given that:
y(0) and dy/dx x^2 y.
(Take h =0.05) 7 7
5. Apply Runge-Kutta method to find an approximate value of y for x 0.2 in steps of
0.1 if dy/dx y^2 ,
given that:
y 1 when x 0.
Evaluate Integral(1 dx, using Simpson's 1/3 rd rule. The upper and lower limits are 6 and 0 7 7
6. A production control superintendent finds the following information on his desk. In departments B and C the number of surplus pallets is 18, 27 and 21 respectively. In departments I and the number of pallets required is 14, 12, 23 and 17 respectively. The time in minutes to move a pallet from one department to another is given below:
To/From G H I J
A 13 25 12 21
B 18 23 14 9
C 23 15 12 16
What is the optimal distribution plan to minimize the moving time?
Solve the following linear programming problem:
Maximize z 2x1 x2
subject to:
x1 2x2 10
x1 x2 6
x1 -x2 2
x1 2X2 1
x1, x2 0 7 7
7. What is the need of dynamic programming and how is it different from linear programming? State some applications of dynamic programming. List down the advantages,
(ii) the applications, and
(iii) the limitations of simulation. 7 7
Other Question Papers
Departments
- Centre for Corporate Education, Training & Consultancy (CCETC)
- Centre for Corporate Education, Training & Consultancy (CCETC)
- National Centre for Disability Studies (NCDS)
- School of Agriculture (SOA)
- School of Computer and Information Sciences (SOCIS)
- School of Continuing Education (SOCE)
- School of Education (SOE)
- School of Engineering & Technology (SOET)
- School of Extension and Development Studies (SOEDS)
- School of Foreign Languages (SOFL)
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Subjects
- Advanced Dynamics Of Machine
- Automobile Engineering
- Combustion Engineering
- Computer Aided Manufacturing
- Computing Aided Design
- Design of Machine Elements
- Engineering Metallurgy
- Engineering Thermodynamics
- Experimental Stress Analysis
- Finite Element Analysis
- Fluid Mechanics
- Heat And Mass Transfer
- Heat Transfer
- I.C. Engines
- Industrial Engineering
- Industrial Ergonomics
- Industrial Measurement And Quality Control
- Industrial Organization And Management
- Kinematics and Dynamics of Machines
- Machine Design - I
- Machine Design-Ii
- Machine Drawing
- Machines Tools
- Maintenance Engineering
- Material Science
- Materials Handling
- Mechanical System Design
- Mechanical Vibration
- Mechanics Of Materials
- Mechatronics
- Metrology
- Metrology And Quality Control
- Non-Conventional Energy Resources
- Non-Destructive Testing
- Nuclear Power Engineering
- Optimisation Techniques In Engineering
- Optimization For Engineering Design
- Power Plant Engineering
- Power Transmitting Elements
- Product Development And Design
- Production And Operations Management
- Production Technology - Ii
- Production Technology-I
- Refrigeration And Air Conditioning
- Refrigeration System
- Robotics
- Safety Engineering
- Technical Entrepreneurship
- Thermal Engineering
- Thermal Engineering - I
- Thermofluid Engineering
- Total Quality Management (Tqm)
- Tribology
- Turbo Machines
- Unconventional Manufacturing Processes
- Welding Engg.