Indian Institute of Technology Kharagpur (IIT-K) 2008 M.Tech Chemical engineering Optimization techniques in process design - Question Paper

INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR *

Date of E>mination: 23.09.2008 (A.N.)    Time: 2 Hours Full Marks: 30.

Mid-Autumn Semester Examinations, 2008-09 5^il Yr. Inted. M.Tech./l^st Yr. M.Tech.

i Subject Name: Optimization Techniques in Process Design Subject No.: CH 62001    No. of Students: 53 of the Deptt. of Chemical Engg.

Instructions:    1. Attempt ALL Questions.

2. All Questions carry equal marks.

3. Assume, if necessary, clearly stating reason.

1. Give brief and to the point answers serially from a to o (Do not rewrite the questions):

a.    When sales are limited by production, how can profit be increased without major modifications in plant?

b.    What is an over-determined optimization problem?

   c. What is a Hessian matrix?

d.    If there are n variables, m inequality constraints and p equality constraints, how many equations will be obtained by KKT conditions for the optimum point?

e.    What happens if the cost function is parallel to one of the inequality constraints?

f.    How is a constraint set expressed mathematically?

g.    If one of the constraints [2xj² - Xi < 6] changes to [- 0.5x₍² + 0.25X2² > 1.5], in a Lagrange Multiplier problem, what will be the changes in the results ?

fiJ)Give an example of Linear Programming problem in industry,

i. Write a Linear Programming problem in standard form, j. What is a Basic Feasible solution ?

. k. What is the Degree of Freedom of a Linear Programming problem ?

1.    What is a Tight inequality constraint ?

m. If there are n variables and m constraints in a Linear Programming problem, then what is the number of Basic Feasible solutions ?

n. What is the relation between gradients of cost and constraint functions at the candidate minimum point ?

.    o. What is meant by equivalent systems of equations ?    7.5

2.    An organic solvent manufacturer produces three blended solvents X, Y and Z by mixing A, B and T, which are fully miscible. He has 20,000 kg of A, 10,000 kg of B and 6000 kg of T in stock. He has orders for 16,000 kg of X, 8,000 kg of Y and 5,000 kg of Z. Profit/kg, mixing losses and raw material requirements are given in the following Table. Formulate the optimization problem to maximize profit._

Product Profit/kg, Rs. Mixing Losses, % Parts/kg of raw materials required A B T X 1.50 2 2 1 1 Y 1.20 4- i 1 1 1 Z 1.00 3 3 1 1

7.5

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Attachment: indian-institute-of-technology-kharagpur--iit-k--2008-m-tech-chemical-engineering-2634-1.JPG

Earning:   Approval pending.