An international manufacturer of electronic products is contemplating introducing a new type of compact disk player. After some analysis of the market, the president of the company concludes that, within 2 years, the new product will have a market share of 5%, 10%, or 15%. The subjective probabilities of these events are .15, .45, and .40, respectively. If the product captures only a 5% market share, the company will lose $28 million. A 10% market share will produce a $2 million profit, and a 15% market share will produce an $8 million profit. If the company decides not to begin production of the new compact disk player, there will be no profit or loss. Based on the expected value decision, what should the company do?
b. The owner of a clothing store must decide how many men’s shirts to order for the new season. For a particular type of shirt, she must order in quantities of 100 shirts. If she orders 100 shirts, her cost is $10 per shirt; if she orders 200 shirts, her cost is $9 per shirt; and if she orders 300 or more shirts, her cost is $8.50 per shirt. Her selling price for the shirt is $12, but any shirts that remain unsold at the end of the season are sold at her famous “half-price, end-of-season sale.” For the sake of simplicity, she is willing to assume that the demand for this type of shirt will be 100, 150, 200, or 250 shirts. Of course, she cannot sell more shirts than she stocks. She is also willing to assume that she will suffer no loss of goodwill among her customers if she understocks and the customers cannot buy all the shirts they want. Furthermore, she must place her order today for the entire season; she cannot wait to see how the demand is running for this type of shirt.
a. Construct the payoff table to help the owner decide how many shirts to order.
b. Draw the decision tree.