An electronics manufacturer faces the decision of how many game console units to order for the coming holiday season. Members of the management team suggested order quantities of 160,000, 175,000, 220,000, or 250,000 units. The wide range of order quantities suggested indicate considerable disagreement concerning the market potential. The product management team asks you for an analysis of the stock-out probabilities for various order quantities, an estimate of the profit potential and to help make an order quantity recommendation. They expect to sell the units for $240 based on a cost of $160 per unit. If console inventory remains after the holiday season, they will sell all surplus inventory for $25 per unit. After reviewing the sales history of similar products, senior sales forecaster predicted an expected demand of 200,000 units with a 0.90 probability that demand would be between 120,000 units and 280,000 units. The senior sales forecaster did not provide the standard deviation but indicated it could be computed from this information with the following hint: The Z score associated with a 90 percent interval such as this is 1.645.

1) Use the senior sales forecasters prediction to define a normal probability distribution that can be used to approximate the demand distribution. In particular, state the mean and standard deviation for a normal distribution based on the information provided by the senior sales forecaster.

2) Compute the probability of a stock-out for the order quantities suggested by the members of the management team. Include a table in your document that summarizes the results of your computations.

3) Compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales = 125,000 units, most likely case in which sales = 200,000 units and best case in which sales = 275,000 units. Calculate an overall expected profit for each of the four order quantities if it is assumed the worst case and best case each have a 5% chance of occurring, respectively.

4) One of QEs managers felt that the profit potential was so great that the order quantity should have a 75% chance of meeting demand and only a 25% chance of any stock-outs. What quantity would be ordered under this policy, and what is the projected profit under the three sales scenarios?