The elevator market is dominated by four suppliers: Otis of the United States, Kone of Finland, Thyssen-Krupp of Germany, and Schindler of Switzerland. Elevators are installed in buildings of a range of heights and incorporate a range of features, resulting in a range of prices from $50,000 to $300,000. After an elevator is installed, the building owner also needs it to be maintained and therefore negotiates a service contract with a price ranging from $2,000 to $5,000 per year. Elevator suppliers make 10% profit on sales and 30% profit on service contracts. Assume that the price ranges for sales and service represent 90% confidence intervals on Normal distributions.

Next year, an elevator supplier projects selling 15,000 elevators and 12,000 new service contracts.

a) What is the expected total revenue from sales and service contracts?

b) What is the expected total profit from sales and service contracts?

c) What is the range of total profits from sales and service contracts? Give a profit range that represents a 90% confidence interval. What assumptions are you making?