1. A pharmaceutical company has 100 kg of chemical 180 kg of B and 120 kg of C available per month. They can use these chemicals to make three pharmaceutical products, namely, 5-5-10 and where the numbers in each case represent the percentage by weight of B and C respectively in each of the products..The cost of these raw materials are given below:
src='./qimages/9153-1.jpg'>

Selling prices of the three products are Rs. 40·50, Rs. 43 and Rs. 45 per kg respectively. There is a capacity restriction of the company for the product as they cannot produce more than 80 kg per month. Determine how much of each of the products they should produce in order to maximize their monthly profit.

2.(a) Explain the direct search method for optimizing multivariable function with equality constraint using a suitable example.
Describe the iterative procedure for the solution of a quadratic programming problem by Wolfe's modified simplex method.

3. Using stepping-stone method, find the optimum solution for the following transportation problem: src='./qimages/9153-3.jpg'>

4.(a) With the help of a suitable example,
explain the Minimax and Maximin Algorithm for decision-making.

(b)A length of wire, 1 m long, is to be divided into two pieces, one in a circular shape and the other into a square, having radius and of side respectively. Find the individual length so that the total area is minimum.

5.(a) Evaluate src='./qimages/9153-5a.jpg'> by using
Simpson's 1/3 rule, and

(ii) Simpson's 3/8 rule.
Using Newton-Raphson method, find the real root of the equation 3x=cosx 1.

6.(a) What is dynamic programming What types of optimization problems can be solved by dynamic programming? Explain.
Differentiate between constrained and unconstrained problems with the help of examples.

7. Write short notes on any two of the following: Integer Programming
Stochastic Programming Genetic Algorithms