A company buys 400 units of an item in a year at a cost of Shs. 5000 per item. The ordering cost is Shs 2000 per order and the carrying cost has being determined to be 20% of the cost of average stock. The company has received a 2% discount offer for the purchase of 100 units or more. Required i. Determine the best inventory policy for the above item (3 marks) b. Five workers are available to work with five machines. The respective costs in Shs associated with each worker and machine is show in the table below. A sixth machine is available to replace one of the existing machines and its associated costs are shown below M W 1 2 3 4 5 6 A 12 3 6 - 5 9 B 4 11 - 5 - 3 C 8 2 10 9 7 5 D - 7 8 6 12 10 E 5 8 9 4 6 - i. Determine whether the new machine 6 can be accepted ( 3 marks) ii. Determine the optimal assignment and saving in cost (3 marks) c. People arrive at a cinema ticket booth in a Poisson distribution arrival rate of 25 per hour. Service time is exponentially distributed with an average time of 2 minutes. Calculate the mean number in the waiting line, the mean waiting time, the mean number in the system, the mean time in the system, the mean time in the system and the utilization factor. ( 4marks) d. ) Below is a transportation problem of a certain commodity has three supply sites A, B and C and four demand locations 1,2,3 and 4. The transportation cost (Ksh) are as follows from To A B C Availability 1 2 7 4 50 2 3 3 1 80 3 5 4 7 70 4 1 6 2 140 Demand 70 90 180 340 i)Find the initial solution and show the allocations in the table and compute the total cost for the solution (6 marks) a. A filling station is being planned and it is required to know how many attendants will be needed to maximize earnings. From traffic studies it has been forecast that customers will arrive in accordance with the following table: Probability of 0 customers arriving in any minute 0.72 Probability of 1 customer arriving in any minute 0.24 Probability of 2 customers arriving in any minute 0.03 Probability of 3 customers arriving in any minute 0.01 From past experience it has been estimated that service times vary according to the following Table ;- Service time in Minutes 1 2 3 4 5 6 7 8 9 10 11 12 Probability 0.16 0.13 0.12 0.10 0.09 0.08 0.07 0.06 0.05 0.05 0.05 0.04 If there are more than two customers waiting, in addition to those being serviced, new arrivals Drive on and the sale is lost. A petrol pump attendant is paid ksh20 per 8 hour day, and the average contribution per customer is estimated to be ksh2. a. How many attendants are needed? (12marks)