Higgenbottom's, a large ski shop in Telluride, Colorado, must place its order for skis within the next week.Their supplier will only accept orders for lots of 1000 pairs of skis.Demand for their skis is strictly dependent on the weather.If the winter is snowy, demand is high, but if the winter is not snowy, demand is low.In snowy winters, they sell about 4,000 pairs of skis; in not snowy winters , they sell about 2,000 pairs.The average pair of skis costs $50 and sells for $80.Leftover skis must be put on sales at the end of season at half price.These half-price sales are always successful and all the skis are sold.

a.Historical records show that 60 percent of the winters in the Rocky Mountains are snowy.How many pairs of skis should the ski shop order?

b.The Rocky Mountain Weather Service Company claims that they can supply a perfect long-range weather forecast for $500.The forecast is based not only on historical trends but also on the scientific extension of present-day weather patterns.Should this service be purchased?

c.The owner of the ski shop decided to check into the accuracy of the Rocky Mountain Weather Service forecasts.It appears that they are far from perfect.Over the last ten years, they have produced 1000 forecasts for various ski areas.When there has been a "snowy" winter for a given area, they have correctly forecasted a snowy winter only 85% of the time.On the other hand, when there has been a "not-so-snowy" winter, their forecast has been correct 90% of the time.How much should the owner of the ski shop be willing to spend for this imperfect information?