Question: A beer distributor owns 20 trucks that have a 90% chance of being in service on any day. New trucks have a 2% chance of

A beer distributor owns 20 trucks that have a 90% chance of being in service on any day.

New trucks have a 2% chance of being out of service (not available for deliveries) on any day.

Demand for deliveries is forecasted to be Normal with an average of 30 truckloads per day and a standard deviation of 5 truckloads per day. If there is a shortage of trucks, the contractor must lease a truck for the day at a cost of $225 per day. New trucks cost $65,000, and as such, the cost of an idle truck is a function of opportunity cost and other similar factors and can be estimated using an 18% APR. Determine the number of new trucks the distributor should purchase.

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