ASSIGNMENT 1

1.       In a factory workshop, machines breakdown at an average rate of 6 per day, the number of breakdowns being Poisson distributed. The present unqualified mechanic can repair motors at an average rate of 8 per day and is paid a daily wage of sh 100. A qualified mechanic offers his services at a daily wage of sh 200 and is capable of repairing, on the average, 10 motors per day. Whenever a motor is idle, there is downtime cost incurrence at the rate of sh 100 per day. Would it be worthwhile to employ the qualified mechanic? Justify on cost/ benefit analysis.                                                                                (5 marks)

2.       Two breakfast food manufacturing firms A and B are competing for an increased market share. To improve their market share both the firms have the following options:

·         Give coupons (strategies a₁ and b₁)

·         Decrease price (strategies a₂ and b₂)

·         Maintain present strategy (strategies a₃ and b₃)

·         Increase advertising ( strategies a₄ and b₄)

The following payoff matrix shows the increase in market share for the firm A.

Advise the firms on the strategies to follow and find the value of the game    (5 marks)

3.       A company manufactures cement in its three factories which is then transported to four distribution centres. The monthly productions of each factory, the demand of each distribution centre and the cost of transporting one tonne are given in the following table:

i)         Suggest the optimal transportation schedule                                 (7 marks)

ii)       Is there any other transportation schedule which is equally attractive? If so, write it.                                                                                                                                (1 mark)

iii)      Build a linear programming model for the problem                                      (2 marks)