Exam Details
| Subject | Structural Optimization | |
| Paper | ||
| Exam / Course | Diploma In Civil Engineering (DCLEVI) / Advanced Level Certificate In Civil Engineering (ACCLEVI) | |
| Department | School of Engineering & Technology (SOET) | |
| Organization | indira gandhi national open university | |
| Position | ||
| Exam Date | December, 2016 | |
| City, State | new delhi, |
Question Paper
Briefly explain concave and convex functions of a single variable.
Describe any four applications of structural optimization.
2. A manufacturing company IS engaged in producing three types of products, B and C. The production department produces, each day, components sufficient to make 50 units of 25 units of Band 30 units of C. The management is confronted with the problem of optimizing the daily production of the products in the assembly department, where only 100 man-hours are available daily for assembling the products. The following additional information is available:
Type of Profit contribution per Assembly Time
products unit of product per product(hrs)
A 12 0.8
B 20 F7
C 45 2.5
The company has a daily order commitment for 20 units of product A and a total of 15 units of products B and C. Formulate the problem as a linear programming model so as to maximize the total profits.
3. Solve the following non-linear programming problem:
Minimize
5x1^1x2^-1 2x1^-1x2^1 5x1^1x2^0 x1^0x2^-1
using the geometric programming method. (Assume n m
Express the mathematical form of Quadratic programming problem.
Write any two applications of Quadratic programming.
5. Determine x1 and x2 so as to
Maximize z =12x1 21x2 2x1x2 -2x1^2 -2x2^2 subject to the constraints
x1
x1+x2 10
x1,x2 0
6. A firm has a total revenue function R =20x-2x^2,and a total cost function C 20, where x represents the quantity. Find the revenue maximizing output level and the corresponding value of profit, price and total revenue.
7. Find the second order Taylor's series approximation of the function
x1^2.x2 5x1 .e^x2
about the point x0=
8. Use dynamic programming to solve the following linear programming problem:
Maximize z 5x2
subject to the constraints
x1
x2
3x1 2x2 18 and
x1,x2 0
What do you mean by slack and surplus variables in linear programming problem?
Obtain the dual of the following primal LP problem:
Maximize z =x1 -2x2 3x3
subject to
-2x1 x2 3x3 2
2x1 3x2 4x3 1
x1 x3 0.
10.(a) What do you mean by Genetic Algorithm What are the building block hypotheses of genetic algorithm
Explain in brief, Crossover and Mutation genetic algorithm.
Describe any four applications of structural optimization.
2. A manufacturing company IS engaged in producing three types of products, B and C. The production department produces, each day, components sufficient to make 50 units of 25 units of Band 30 units of C. The management is confronted with the problem of optimizing the daily production of the products in the assembly department, where only 100 man-hours are available daily for assembling the products. The following additional information is available:
Type of Profit contribution per Assembly Time
products unit of product per product(hrs)
A 12 0.8
B 20 F7
C 45 2.5
The company has a daily order commitment for 20 units of product A and a total of 15 units of products B and C. Formulate the problem as a linear programming model so as to maximize the total profits.
3. Solve the following non-linear programming problem:
Minimize
5x1^1x2^-1 2x1^-1x2^1 5x1^1x2^0 x1^0x2^-1
using the geometric programming method. (Assume n m
Express the mathematical form of Quadratic programming problem.
Write any two applications of Quadratic programming.
5. Determine x1 and x2 so as to
Maximize z =12x1 21x2 2x1x2 -2x1^2 -2x2^2 subject to the constraints
x1
x1+x2 10
x1,x2 0
6. A firm has a total revenue function R =20x-2x^2,and a total cost function C 20, where x represents the quantity. Find the revenue maximizing output level and the corresponding value of profit, price and total revenue.
7. Find the second order Taylor's series approximation of the function
x1^2.x2 5x1 .e^x2
about the point x0=
8. Use dynamic programming to solve the following linear programming problem:
Maximize z 5x2
subject to the constraints
x1
x2
3x1 2x2 18 and
x1,x2 0
What do you mean by slack and surplus variables in linear programming problem?
Obtain the dual of the following primal LP problem:
Maximize z =x1 -2x2 3x3
subject to
-2x1 x2 3x3 2
2x1 3x2 4x3 1
x1 x3 0.
10.(a) What do you mean by Genetic Algorithm What are the building block hypotheses of genetic algorithm
Explain in brief, Crossover and Mutation genetic algorithm.
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- Advanced Steel Design
- Air Quality Monitoring And Control
- Analysis And Design Of Bridges
- Construction Supervision And Building Maintenance
- Earthquake Engineering
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- Elements Of Soil Dynamics And Machine Foundation
- Environment Impact Analysis Of Civil Engineering Projects
- Irrigation Engineering
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- Structural Optimization
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