answer from 6B down

answer all about number 6

QUESTION 6 (a) ) What do you understand by Markov chains? (1 mark) (1) Discuss briefly two areas of management where Markow chains Have Beertalled successfully. [2 marks) (b) A market survey is made on three brands of breakfast foods XY and Z. Every time the customer purchases a new package, he may buy the same brand or switch to another brand. The following estimates are obtained as decimal fractions Brand just purchased Z 0.2 03 005 03 0.3 Present brand Y Z At this time it is estimated that 30 percent of the people buy brand X. 20 percent brand and 50 percent brand Z Draw the Markov chain diagram for the given one step transition probability mat. marks) (m) What will the distribution of customers be after two time periods 2 marlis) (m) Find the steady state distribution of customers QUESTION 7 (a) Show whether the function is convex, concave or neither f(x) = 4x3 - 3x (b) Use the method of Lagrange multipliers to solve the following onlinear programming problem (NLPP). Does the solution maximize or minimize the objective function Optimize Z = 7% - 0.3x} + 8x2 - 0.423 subject to 4x + 5x2 = 100 and X1,42 20 QUESTION 6 (a) ) What do you understand by Markov chains? (1 mark) (1) Discuss briefly two areas of management where Markow chains Have Beertalled successfully. [2 marks) (b) A market survey is made on three brands of breakfast foods XY and Z. Every time the customer purchases a new package, he may buy the same brand or switch to another brand. The following estimates are obtained as decimal fractions Brand just purchased Z 0.2 03 005 03 0.3 Present brand Y Z At this time it is estimated that 30 percent of the people buy brand X. 20 percent brand and 50 percent brand Z Draw the Markov chain diagram for the given one step transition probability mat. marks) (m) What will the distribution of customers be after two time periods 2 marlis) (m) Find the steady state distribution of customers QUESTION 7 (a) Show whether the function is convex, concave or neither f(x) = 4x3 - 3x (b) Use the method of Lagrange multipliers to solve the following onlinear programming problem (NLPP). Does the solution maximize or minimize the objective function Optimize Z = 7% - 0.3x} + 8x2 - 0.423 subject to 4x + 5x2 = 100 and X1,42 20