X Garage is the best-selling Mercedes-Benz dealer in the west of the island. In the past 36 months, its sales have ranged from a minimum of 6 new cars to a maximum of 12 as reflected in the table below.

X Grage considers that its sales will continue with the same pattern for the next 24 months and that delivery times will continue at the same rate as also indicated in the table, in the form of probabilities.

The garage's current policy is to order 14 cars at a time since this completes the load of two trucks, 7 cars each. In addition, a new order is placed each time the inventory reaches 12 cars.

a) Determine the results of these inventory policies, in terms of average demand, average delivery time, final inventory and average number of lost sales when simulating for the next two years. Arbitrarily assume the initial inventory that you deem appropriate.

b) Consider that the ABC garage has established the following relevant costs: (1) Monthly cost of keeping a Mercedes in inventory: $ 600 (2) Average cost of lost sale: $ 4,350 and (3) Cost of processing an order: $ 570. What is the total cost of inventory per month under the simulated policy in part (a)?

Sales of New Cars/Month Frequency 6. 3 7 4 8 6. 9. 12 10 9 11 1 12 1 36 months