A luxury car dealer must pay $20,000 for each car purchased. The annual holding cost is estimated to be 25% of the dollar value of inventory. The dealer sells an average of 500 cars per year. He is...

A luxury car dealer must pay $20,000 for each car purchased. The annual holding cost is estimated to be 25% of the dollar value of inventory. The dealer sells an average of 500 cars per year. He is willing to backlog some demand but estimates that if he is short one car for one year, he will lose $20,000 worth of future profits. Each time the dealer places an order for cars, the ordering cost is $10,000. Determine the luxury car dealer’s optimal ordering policy. What is the maximum shortage that will occur? Assume it costs $5000 to store a car for a year (this is in addition to the holding cost above).