Members of a management team suggested order quantities of 15,000, 18,000, 24,000, or 28,000 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 probabilites for various order quantities, an estimate of the profit potential, and to help make an order quantity recommendation. Specialty (the company name) expects to sell Weather Teddy (the product) for $24 based on a cost of $16 per unit. If inventory remains after the holiday season, Specialty will sell all surplus inventory for $5 per unit. After reviewing the sales history of similiar products, Specialty's senior sales forecaster predicted an expected demand of 20,000 units with a 0.90 probability that demand would be between 10,000 units and 30,000 units.

1. Use the sales forecaster's rediciton to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.

2. Compute the probability of a stock-out for the order quantities suggested by members of the management team.

3. Compute the projected profit for the rder quantities suggested by the management team under three scenarios: worst case in which sales = 10,000 units, most likely case in which sales = 20,000 units, and best case in which sales = 30,000 units.

4. One of Specialty's managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock-outs. What quantity would be ordered under this policy, and what is that projected profit under the three sales scenarios.

5. Provide your own recommendation for an order quantity and note the associated profit projections. Provide a rationale for your recommendation.