Kathryn Marley owns and operates the largest Mercedes- Benz auto dealership in Pittsburgh. In the past 36 months, her sales have ranged from a low of 6 new cars to a high of 12 new cars, as reflected in the following table:
SALES OF CAR MONTH ... FREQUENCY
6 ............... 3
7 ............... 4
8 ............... 6
9 ............... 12
10 ............... 9
11 ............... 1
12 ............... 1
36 month

Marley believes that sales will continue during the next 24 months at about the same historical rates, and that delivery times will also continue to follow the following pace (stated in probability form):
Delivery Time (Month) ... Probability
1 ............ 44
2 ............ 33
3 ............ 16
4 ............ 07
100
Marley’s current policy is to order 14 cars at a time (two full truckloads, with 7 autos on each truck), and to place a new order whenever the stock on hand reaches 12 autos.
a) What are the results of this policy when simulated over the next 2 years?
b) Marley establishes the following relevant costs:
(1) Carrying cost per Mercedes per month is $ 600;
(2) Cost of a lost sale averages $ 4,350; and
(3) Cost of placing an order is $ 570. What is the total inventory cost of this policy?