Process Modelling, Simulation and Optimization — Summer 2023

Explain the meaning of following terms for optimization: Feasible solution, feasible region, optimal solution.

Describe the major obstacles to optimization problem.

List the six general steps for the analysis and solution of optimization problem.

Explain various applications of modelling and simulation.

Abox with a square base and open top is to hold 1000 cm3. Find the dimensions that require the least material (assume uniform thickness of material) to construct the box.

Discuss the optimizing recovery of waste heat with suitable figure and equations.

Explain the features of Basic Tearing Algorithm.

Explain equation solving approach in brief.

Explain white box model.

Develop batch reactor model.

Explain the importance of degree of freedom in model building.

Differentiate between steady state and dynamic simulation.

What is sequential modular approach in simulation? Explain the step with diagram.

Explain the uses of mathematical models.

Explain the penalty methods for solving nonlinear programming with constraints.

Develop the equations for the series of isothermal, variable holdup CSTRs. List all the assumptions with their justifications.

Explain simplex search method.

Determine positive-definiteness of a function f(x) = 2x2 −3x x + 2x2.

Explain in brief how one-dimensional search is applied in a multidimensional problem.1

Explain Lagrange multiplier method.

Explain the necessary and sufficient conditions for an extremum of an unconstrained function.

Minimize function f(x) =x4−x+1 using Newton’s method for starting point of x = 3 show five iterations.

Minimize the quadratic function f(x) = x2−x using finite difference newton method start with x = 3 and h = 0.001.

Write a short note on decomposition of networks.

Solve the following linear programming problem using simplex method Maximize Z = 6x + 5 x12 Subject to x + x ≤ 512 3x + 2x ≤12 x ,x ≥