Tesla is trying to determine the proper capacity level for a new electric car. Below are the details of the problem.

A unit of capacity provides the potential to produce one car per year. Production of a car is dependent upon demand and capacity. A car will only be produced if there is demand AND enough capacity. (No inventory is ever built up.)

It costs $20,000 to build a unit of capacity and the cost is charged equally over the next 5 years ($4,000 a year).

It also costs $800 per year to maintain a unit of capacity (whether or not it is used).

Each car sells for $44,000 and incurs a variable production cost of $35,000.

The annual demand for the electric car during each of the next 5 years is believed to be normally distributed with mean 750,000 and standard deviation 150,000. The demands during different years are assumed to be independent.

We are working with a 5-year planning horizon. (Ignore the time value of money.) Capacity levels of 600,000, 700,000, 800,000, 900,000, and 1,000,000 are under consideration.

Use 1000 samples to determine the best capacity level, using profit as your target to analyze.

Provide a 98% confidence interval for the expected profit at your best capacity level.