JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III OPTIMIZATION TECHNIQUES Previous Question Paper (May - 2019 - R16)

B.Tech | III | III-II | R16 | May - 2019

Answer PaperPaper Code: 136FRMaximum Marks: 75Time: 3 hours

Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.

Part A

125 marks
a

Define the term optimization.

2 marks

Answer

Optimization is the process of finding the best solution or set of values for a given objective function, subject to a specific set of constraints, to either maximize or minimize the outcome.

b

Classify various optimization problems.

3 marks

Answer

Optimization problems can be classified based on:

  • The nature of the objective function and constraints (Linear vs. Non-linear).
  • The nature of the variables (Continuous vs. Integer/Discrete).
  • The presence of constraints (Constrained vs. Unconstrained).
  • The nature of the equations (Deterministic vs. Stochastic).
c

When does degeneracy occur in Transportation Problem?

2 marks

Answer

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d

Bring out the relation between LPP and Transportation problem.

3 marks

Answer

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e

What is interpolation?

2 marks

Answer

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f

Classify one dimensional minimization methods of optimization.

3 marks

Answer

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g

What do you understand by the term ‘penalty’?

2 marks

Answer

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h

Differentiate between the interior and exterior penalty function methods.

3 marks

Answer

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i

What are the applications of dynamic programming?

2 marks

Answer

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j

Write a short note on Recursive relation and Return function with reference to dynamic programming approach.

3 marks

Answer

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Part B

2

Minimize

z = 3x12 + 4x22
Subject to
2x1 – 3x2 = 10
By using Lagrangian multiplier method.

10 marks

Answer

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OR
3

Consider the problem: Maximize

f(x,y) = x2 + (y – 1)2
Subject to
g1 = y3 – 2x ≤ 0; g2 = y3 + 2x ≤ 0.
Determine whether the constraint qualification and Kuhn–Tucker conditions are satisfied at the optimum point.

10 marks

Answer

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4

An oil refinery can blend two grades of crude oil to produce quality P and Q petrol. Two possible blending processes are available. For each production run, the older process uses 5 units of crude A, 7 units of crude B and 2 units of crude C to produce 9 units of P and 7 units of Q. The newer process uses 3 units of crude A, 9 units of crude B and 4 units of crude C to produce 5 units of P and 9 units of Q petrol. Because of prior contract commitments the refinery must produce at least 500 units of P and at least 300 units of Q for the next month. It has available 1500 units of crude A, 1900 units of crude B and 1000 units of crude C. For each unit of P the refinery receives rs. 60 while for each unit of Q if receives rs. 90. Find out the linear programming formulation so as to maximize the revenue.

10 marks

Answer

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OR
5

A dealer stocks and sells four types of Bicycles namely Atlas, Bharath, Champion, Duncan which he may procure from three different suppliers namely Priyanshu, Qureshi and Raju. His anticipated sales for the bicycles for the coming seasons are 410, 680, 310 and 550 nos. respectively. He can obtain 900 bicycles from Priyanshu, 600 from Qureshi and 560 from Raju at suitable prices. The profit per bicycle for each supplier is tabulated below:

SupplierAtlasBharathChampionDuncan
Priyanshu (P)21.5026.0019.5021.00
Qureshi (Q)20.5024.0020.0021.00
Raju (R)18.0019.5019.0019.50

Formulate the above information as transportation model and obtain initial solution by North West Corner Rule.

10 marks

Answer

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6

Perform four iterations of Powell’s method to minimize the function:

f(x1, x2) = 100(x2 – x12)2 + (1 – x1)2
from the starting point (0,0).

10 marks

Answer

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OR
7

Perform ‘three’ iterations of Univariate Method to minimize the function

f(x1, x2, x3) = x12 + 2x22 + (x32 / 3)
with starting point as (-1, 1, 2).

10 marks

Answer

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8

Solve the following nonlinear programming problem using the exterior penalty function method:

Minimize

f(x, y, z) = xyz

Subject to

x + y ≤ 45; 6 ≤ z ≤ 18

10 marks

Answer

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OR
9

Maximize

f(x1, x2) = 2x12 + 3x22
Subject to
3 – x1 ≤ 0; – x2 ≤ 0
by using the interior penalty function method.

10 marks

Answer

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10

Find the longest path between the points A and N by solving the dynamic programming problem.

10 marks

Answer

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OR
11

An employee located at city A is transferred to city I. He gets reimbursement of his travel expenditures on the shortest route. The possible alternative routes and the distances between any two cities are given. Determine the shortest route that the employee must travel. Also, find the shortest routes from various cities to city I.

10 marks

Answer

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About this paper

This page contains the question paper of OPTIMIZATION TECHNIQUES from JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD for B.Tech CE III III-II, May - 2019, R16.

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