The Westlands Members Club receives 30 copies of the High Society magazine every week. This magazine is currently sold for Shs.150 while the cost is Shs. 90. Unsold magazines in a given week are sold the following week to a paper recycling plant for Shs.5.70 each.

The weekly demand for the High Society magazine fluctuates according to the following probability distribution.

                               Demand           Probability

                                    28                        .15

                                    29                        .18

                                    30                        .25

                                    31                        .22

                                     32                     .20

Required:

(a) Using the random numbers provided below, perform simulations of sales of this magazine for 12 weeks and then answer the following questions.                                                                                      [5Marks]

(b) Find:

  (i) The average number of papers sold each week.           

  (ii) The average number of unsold papers per week.

  (iii) The demand on the 12^th week.

  (iv)The average weekly profit.

  (v) The probability that a given copy of the magazine will be sent to the recycling

       plant.

  (vi) The probability that a given customer will come to the Club and find no copy

        of High Society magazine when he/she wants one.

  (vii) The probability that, at the end of any given week, the recycling plant will be   contacted for delivery (i.e. the chance for any leftovers).

  viii) The probability that demand = supply in any given week.

        Assign the range numbers starting with 00.