A car importer has three cars left of a particular model. A car dealer wants to buy two cars. The Dealer has a buyer who undertook to pay a total of $150,000 for the two cars. The price offered by the importer to the dealer today is $50,000 per car. If the car dealer decides not to buy today, there is a 0.3 chance that no car will be sold by next week, a 0.4 chance that one car will be sold by next week and a 0.3 chance that two cars will be sold by next week. Next week, the cars that were not sold for sale will be priced at $40,000 each. The dealer can buy two cars at this price (if they are still in the hands of the importer) or wait another week. If the importer has all three cars left, the chances of selling this week are the same as in the first week. If he has two cars left, the chance of none being sold is 0.6. At the end of the second week, the remaining cars will be put up for sale at a price of $30,000 each. In any case, the dealer will not buy only one car from the importer (the customer is interested in two cars and no less). . What is the optimal purchase / waiting policy of the car dealer and what is the expected profit expectation for him under this policy