Specialty Toys, Inc. sells a variety of new and innovativechildren’s toys. Management learned that the preholiday season isthe best time to introduce a new toy, because many families usethis time to look for new ideas for December holiday gifts. WhenSpecialty discovers a new toy with good market potential, itchooses an October market entry date. In order to get toys into itsstores by October, Specialty places one-time orders with itsmanufacturers in June or July of each year. Demand for children’stoys can be highly volatile. If a new toy catches on, a sense ofshortage in the marketplace often increases the demand to highlevels and large profits can be realized. However, new toys canalso flop, leaving Specialty stuck with high levels of inventorythat must be sold at reduced prices. The most important questionthe company faces is deciding how many units of a new toy should bepurchased to meet anticipated sales demand. If too few arepurchased, sales will be lost; if too many are purchased, profitswill be reduced because of low prices realized in clearance sales.For the coming season, Specialty plans to introduce a new productcalled Weather Teddy. This variation of a talking teddy bear ismade by a company in Taiwan. When a child presses Teddy’s hand, thebear begins to talk. A built-in barometer selects one of fiveresponses that predict the weather conditions. The responses rangefrom “It looks to be a very nice day! Have fun†to “I think it mayrain today. Don’t forget your umbrella.†Tests with the productshow that, even though it is not a perfect weather predictor, itspredictions are surprisingly good. Several of Specialty’s managersclaimed Teddy gave predictions of the weather that were as good asthose of many local television weather forecasters. As with otherproducts, Specialty faces the decision of how many Weather Teddyunits to order for the coming holiday season. Members of themanagement team suggested order quantities of 15,000, 18,000,24,000, or 28,000 units. The wide range of order quantitiessuggested indicates considerable disagreement concerning the marketpotential. The product management team asks you for an analysis ofthe stock-out proba- bilities for various order quantities, anestimate of the profit potential, and help with mak- ing an orderquantity recommendation. Specialty expects to sell Weather Teddyfor $24 based on a cost of $16 per unit. If inventory remains afterthe 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 of20,000 units with a .95 probability that demand would be between10,000 units and 30,000 units.
Prepare a managerial report that addresses the following issuesand recommends an order quantity for the Weather Teddy product.
1. Use the sales forecaster’s prediction 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 orderquantities suggested by members of the management team.
3. Compute the projected profit for the order quantitiessuggested by the management team under three scenarios: worst casein 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 potentialwas so great that the order quantity should have a 70% chance ofmeeting demand and only a 30% chance of any stock-outs. Whatquantity would be ordered under this policy, and what is theprojected profit under the three sales scenarios?
5. Provide your own recommendation for an order quantity andnote the associated profit projections. Provide a rationale foryour recommendation.
