Members of a management team suggestedorder quantities of 15,000, 18,000, 24,000, or 28,000 units. The wide range of order quantities suggested indicate considerabledisagreement concerning the market potential. the productmanagement team asks you for an analysis of the stock-outprobabilites for various order quantities, an estimate of theprofit potential, and to help make an order quantityrecommendation. Specialty (the company name) expects to sellWeather Teddy (the product) for $24 based on a cost of $16 perunit. If inventory remains after the holiday season, Specialty willsell all surplus inventory for $5 per unit. After reviewing thesales history of similiar products, Specialty's senior salesforecaster predicted an expected demand of 20,000 units with a 0.90probability that demand would be between 10,000 units and 30,000units.

1. Use the sales forecaster's rediciton to describe a normalprobability distribution that can be used to approximate the demanddistribution. Sketch the distribution and show its mean andstandard deviation.

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

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

4. One of Specialty's managers felt that the profit potential wasso 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 notethe associated profit projections. Provide a rationale for your recommendation.