As with other products, Specialty faces the decision of how many Weather Teddy units to order

for the coming holiday season. Members of the management team suggested order quantities of 15,000,

18,000, 24,000, or 28,000 units. The wide range of order quantities suggested indicates 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. Specialty expects to sell Weather Teddy 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 similar products, Specialty's senior sales forecaster

predicted an expected demand of 20,000 units with a .95 probability that demand would be between

10,000 units and 30,000 units.

Managerial Report

Prepare a managerial report that addresses the following issues and recommends an order quantity for the

Weather Teddy product.

1. Use the sales forecaster's prediction 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 order 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 the 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.

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I started this problem and believe I did numbers 1 and 2 correctly but would like someone to check my solutions so I know I am on the right track or I missed the mark which will result in the rest of the questions being wrong.