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###### Math · Statistics And Probability
Question details

Novelty Toys, Inc. sells a variety of new and innovative children’s toys. Management learned that the preholiday season is the best time to introduce a new toy, because many families use this time to look for new ideas for December holiday gifts. When Novelty discovers a new toy with good market potential, it choses an October market entry date.

In order to get toys in its stores by October, Novelty places one-time orders with its manufactures in July of each year. Demand for children’s toys can be highly volatile. If a new toy catches on, a sense of shortage in the marketplace often increases the demand to high levels and large profits can be realized. However, new toys can also flop, leaving Novelty stuck with high levels of inventory that must be sold at reduced prices. The most important question the company faces is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales.

For the coming season, Novelty plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear is made by a company in Taiwan. When a child presses Teddy’s hand, the bear begins to talk. A built-in barometer selects one of five responses that predict weather conditions. The responses range from “It looks to be a very nice day! Have fun” to “I think it may rain today. Don’t forget your umbrella”. Tests with the product show that, even though it is not a perfect weather predictor, its predictions are surprisingly good. Several of Novelty’s managers claimed Teddy gave predictions of the weather as good as local television weather forecasters.

As with other products, Novelty 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 asked 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. Novelty 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 inventories for \$5 per unit. Novelty’s sales forecaster predicted the demand for Weather Teddy with an expected value of 20,000 units and a standard deviation of 5,100 units.

One of Novelty’s managers felt that the profit potential was so great that the order quantity should have a 60% chance of meeting demand and only a 40% chance of any stock-out. What quantity would be ordered under this policy, and what are the projected profits under the three sales scenarios?.

Let Q be the 60% - 40% order quantity. Using the relation P(D £ Q) = 0.6, find Q. To get a full credit, use Excel function NORM.INV; see page 286. After finding Q, compute the corresponding projected profits under the three demand scenarios.