Download AKTU B-Tech 6th Sem 2015-2016 NME 011 Engineering Optimization Question Paper

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NME-011

(Following Paper ID and Roll No. to be filled in your Answer Books)

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Paper ID: 140661

Roll No.

B.TECH.

Theory Examination (Semester-VI) 2015-16

ENGINEERING OPTIMIZATION

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Time: 3 Hours

Max. Marks : 100

Section-A

1. Attempt all questions. All questions carry equal mark. Write answer of each question in short. (2×10=20)
   1. Write the linear programming problem in standard form.
   2. What is a Pivot operation?
   3. State the Kuhn-Tucker conditions.

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   4. What is the difference between Newton and Quasi-Newton method?
   5. What is the limitation of the linear extended penalty function?
   6. How is the direction-finding problem solved in Zoutendijk's method?

Section-B

Attempt any five questions from this section. (10×5=50)

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1. Maximize f = x1+2x2+x3 Subject to 2x1+x2-x3=2 -2x1+x2-5x3=-6 x1+2x2+x3=6 x?= 0, i = 1, 2, 3 Using simplex method.
2. Minimize f (x1, x2) = (x1-1)² – x2² Subject to g1 (x1, x2) = x1³ – 2x2=0 g2 (x1, x2) = x1³ + 2x2=0
3. Solve the following Integer programming problem. Using the cutting plane method. Take the convergence limit in step 5 as e = 0.02.
4. Derive the expression for solution of an Unconstrained Geometric Programming program using Differential Calculus.
5. In a certain reservoir pump installation, the first cost of the pipe is given by (100 D+ 50 D²), where D is the diameter of the pipe in cm. The cost of the reservoir decreases with an increase in the quantity of fluid handled and is given by 20/Q, where Q is the rate at which the fluid is handled (cubic meters per second). The pumping cost is given by (300Q² /D5). Find the optimal size of the pipe and the amount of fluid handled for minimum overall cost.

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6. Minimize f(x1,x2) = x1²-x1+2x1²+2x1x2+x2² starting from the point X0 using CAUCHY METHOD.
7. What are the Rank 1 and Rank 2 Updates in QUASI-NEWTON Methods?

Section-C

Attempt any two questions from this section. (15×2=30)

1. Explain the Exterior Penalty Function Method with suitable example.
2. Solve the following LP problem using the branch and bound method: Maximize f = 3x1+4x2 Subject to 7x1+11x2=88 3x1-x2= 12 x1=0 x2=0

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3. Design a helical spring for minimum weight subject to a constraint on the shear (t) induced in the spring under a compressive load P.

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