JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III OPTIMIZATION TECHNIQUES Previous Question Paper (May - 2019 - R16)
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
Define the term optimization.
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.
Classify various optimization problems.
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).
When does degeneracy occur in Transportation Problem?
Answer
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Bring out the relation between LPP and Transportation problem.
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What is interpolation?
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Classify one dimensional minimization methods of optimization.
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What do you understand by the term ‘penalty’?
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Differentiate between the interior and exterior penalty function methods.
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What are the applications of dynamic programming?
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Write a short note on Recursive relation and Return function with reference to dynamic programming approach.
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Part B
Minimize
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Consider the problem: Maximize
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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.
Answer
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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:
| Supplier | Atlas | Bharath | Champion | Duncan |
|---|---|---|---|---|
| Priyanshu (P) | 21.50 | 26.00 | 19.50 | 21.00 |
| Qureshi (Q) | 20.50 | 24.00 | 20.00 | 21.00 |
| Raju (R) | 18.00 | 19.50 | 19.00 | 19.50 |
Formulate the above information as transportation model and obtain initial solution by North West Corner Rule.
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Perform four iterations of Powell’s method to minimize the function:
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Perform ‘three’ iterations of Univariate Method to minimize the function
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Solve the following nonlinear programming problem using the exterior penalty function method:
Minimize
Subject to
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Maximize
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Find the longest path between the points A and N by solving the dynamic programming problem.
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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.
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