QUESTION SIX 10 Define the following terma is used in Markoviin analysing i Transition maira. ") Initial Probability vector " Equilibrium wv) Absorbing size bj A company employs four clauses of machine operators (A,B.C.Dj: all new employees are hired as clan D and, through a spotem of promotion, may work up to a higher class, Currently, there are 200 chin D. 150 class C. 90 class B and 60 class A employees, The company has signed an agreement with the union specifying that 10 percent of all employees in each clan be promoted, one class in each year, Statistics show that each year 15 percent of the clans D employees are separated from the company by remon muchin retirement, resignation and death, Similarly 15 percent of class C, 10 percent of class B and 5 percent of class A employees are also separated. For each employee lost, the company hires a new clans D employer. Required: The transition matrix. in The number of employers in each class two years after the agreement with the union, lily The equilibrium state in number of employees, (Q 2 June 2107) QUESTION SEVEN " Two firms A and B in Nairoly Industrial area make ghie, The cost functions for making glue for the run firms are as folkrage C=02 + 300 Firm B - C=0m + 50 Where a- is hires of gluc produced in 100. Required By drawing a graph of house functions, show whose firm's costs increase more rapidly bj On the trudy of costs and revenue for production of him pens by a small company ACO Lid, the fulbrewing expressions were determined, Before production stars a set-up cost of Sh 1500 existed. AR = 600 - 0.54 MC = 141- Bq + 0.150 Marginal ant Requiresh The caption for profit. ill At what quantity q is profit mimired. illy In his quantity q also the point the revenue is maximized? QUESTION EIGHT " Explain the following terms as uned in calculup Turning point, in Second under denative condition. in Partial derivative. wv) Mixed partial derivative. v) Saddle point bj Drumstick Chicken Wings Led supplies chicken wings for Kaku Inn with doe following demand and cust Functions for a given urck - Price TC - 50 + 31,0m - Total cost Where 4 - number of chicken wings supplied. Required Toul revenue for Drummich Chicken Wing Lid. In) Deeremine the number of chicken wings that maximize weekly profit. In What is the difference in profit if the Drumstick Chicken Wings Lid. objective is in maximiar revenue rather than proficiQUESTION NINE When the filling input - ourpoor martin and demand vector of thees S, rubber Band due G inchairs, 12 0:4QUESTION FIVE Moving averages are often used in an effort to identify movements in share prices. Approximate monthly closing prices (in Sh. per share) for Toys Children Lid. for December 2000 through November 2001 are shown below:Month Price (Sh.) December 2000 40 January 2001 38 February 2001 39 March 2001 41 April 2001 36 May 2001 41 June 2001 34 July 2001 37 August 2001 35 September 2001 37 October 2001 40 November 2001 41 Required: a) Use a 3-month moving average to forecast the closing price for December 2001. b) Use a 3-month weighted moving average to forecast the closing price for December 2001. Use weights of 0.4 for most recent period, 0.4 for the second period back and 0.2 for the third period back. c) Use exponential smoothing constant of a = 0.35 to forecast the closing price for December 2001. d) Which of the three methods do you prefer? Why? (Q 5 Dec 2001)