Download GTU B.Tech 2020 Summer 8th Sem 2180503 Process Modeling, Simulation And Optimization Question Paper

GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VIII EXAMINATION- Summer 2020
Subject Code: 2180503 Date: 27/10/2020

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Subject Name: PROCESS MODELING, SIMULATION & OPTIMIZATION
Time: 02:30 PM TO 05:00 PM Total Marks: 70

Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.

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3. Figures to the right indicate full marks.

Q.1 (a) Draw the flow chart for implementing Fibonacci method. 03
(b) Show the advantages and disadvantages of Newton’s method. 04
(c) What is Optimization? List the six general steps for the analysis and solution of optimization problems. 07

Q.2 (a) Explain the meaning of following terms for optimization: Feasible solution, feasible region, optimal solution. 03

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(b) What is simulation? Explain linear system analysis. 04
(c) Discuss the degree of freedom analysis with suitable example. 07
OR
(c) Explain the attributes of the process affecting costs/profits make them attractive for the application of optimization 07

Q.3 (a) Minimize f(x) = x* — x + 1 using Newton’s method. Take starting point = 0.64. 03

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(b) Explain equation oriented mode in simulation. 04
(c) For modular approach to process simulation, discuss sequential modular approach in detail. 07
OR
(a) Determine whether the following function is convex or concave:
() = 4x? +3x3 + 5x2 + 6y %, + X309 3%; — 2%, + 15 03

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(b) Define the different measures of profitability/economic performance along with their significance. 04
(c) Explain partitioning and tearing with.example. 07

Q.4 (a) Find the Eigen value Hessian matrix for f(x) = 2x,2 + 3xix2 — 2x2 + 15. 03
(b) List out limitation of Region elimination methods. Compare different region elimination methods and suggest best method for initial interval of 3.5 for accuracy of 0.1. 04
(c) Discuss optimization of evaporator design. 07

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OR
(a) Write different conditions for a given function to be convex or concave in tabular form. 03
(b) Minimize f(x) = 4Xs? + 5Xz2 subject to 2X4 + 3Xz — 6 = 0 using Lagrange Multipliers method. 04
(c) List out multivariable analytical methods for optimization problems with restricted variables equality constraints and explain any one of them with example. 07

Q.5 (a) A poster is to contain 300 cm? of printed matter with margin of 6 cm at the top and bottom and 4 cm at each side. Find the overall dimensions that minimize the total area of poster. 03

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(b) Discuss Distributed V/S Lumped Parameter models. 04
(c) List out the important model building steps for a process. 07
OR
(a) Classify the following function that they are convex or concave. f(x) = 2x] — 3x,x, + 2x3 03
(b) Explain Simultaneous modular approach in simulation. 04

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(c) Discuss essential feature of optimization problem. 07

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