Explain physical vs mathematical modeling.
[3 marks]Write in brief on uses and scope of mathematical models.
[4 marks]Find extreme points of f(x₁,x₂) = x₁³ + x₂³ + 2x₁² + 4x₂² + 6.
[7 marks]Define deterministic and stochastic processes.
[3 marks]Explain fundamental laws used in modeling.
[4 marks]Derive model of batch reactor for first order series reaction A → B → C
[7 marks]Derive mathematical model of an isothermal CSTR with constant holdup
[7 marks]Define feasible solution, feasible region, and optimum solution.
[3 marks]Explain the geometry of linear programs.
[4 marks]Fit the exponential curve the following data using Least Square method: y x 25 38 56 84
[7 marks]Explain partitioning with example.
[3 marks]Explain the algorithm of steepest descent method for unconstrained multivariable optimization problem.
[4 marks]Explain fitting of VLE data by non linear regression
[7 marks]Distinguish between sequential & simultaneous modular approaches.
[3 marks]Differentiate between Black box model, grey box model and white box model with proper example
[4 marks]It is required to design a close-topped rectangular tank whose total area is to be 110 m2 . If a maximum volume is required then formulate the problem. Page 1 of
[2 marks]Explain advantages of working with modern process simulators.
[3 marks]Explain Simplex algorithm for linear programming.
[4 marks]Minimize the quadratic function: f(x) = x2 – x using quasi-newton method with initial guess x=3
[7 marks]Give essential features of optimization problems.
[3 marks]Explain algorithm of Golden section method.
[4 marks]Explain the steps for finding the optimum L/Dratio for a pressurized cylindrical storage vessel. List all the variables and the important assumptions.
[7 marks]Discuss general procedure for solving optimization problems.
[3 marks]Differentiate steady state and dynamic simulators and give examples of each.
[4 marks]What is Optimization? List the six general steps for the analysis and solution of optimization problems Page 2 of
[2 marks]