Lily’s Gourmet Ice Cream Shop offers a variety of gourmet ice cream and shakes. Although Lily’s competes with other ice cream shops and frozen yogurt stores, none of them offer gourmet ice creams with a wide variety of different flavors. The shop is also located in an upscale area and therefore can command higher prices. The owner is a culinary school graduate without much business experience and has engaged the services of one of her friends who recently obtained an MBA to assist her with financial analysis of the business and evaluation of the profitability of introducing a new product. The shop is open during the spring and summer, with higher sales in the summer season. Based on past observation, Lily has defined three sales scenarios for the new product 

Summer: 

■ High—3,000 units 

■ Most likely—2,500 units 

■ Low—2,100 units 

Spring: 

■ High—2,500 units 

■ Most likely—1,500 units 

■ Low—1,000 units 

The expected price is $3.00. However, the unit cost is uncertain, and driven by the costs of the ingredients she has to buy for the product. This is estimated to be between $1.40 and $2.00, with a most likely value of $1.50 in the summer, but in the spring, the most likely cost is $2.00 because the ingredients are more difficult to obtain then. Fixed costs are estimated to be $2,600. Find the distribution of profit for each season and the annual profit distribution using 200 trials for each.