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We are trying to determine the proper capacity level for a new electric car. Think of this as how large should we build our factory to manufacture electric cars. Below are the details of the problem.

A unit of capacity gives us 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.

It costs $$10,000$ to build a unit of capacity and the cost is charged equally over the next $5$ years $($$$2,000$ a year$).$

It also costs $$400$ per year to maintain a unit of capacity $($whether or not it is used$).$

Each car sells for $$14,000$ and incurs a variable production cost of $$10,000.$

The annual demand for the electric car during each of the next $5$ years is believed to be normally distributed with mean $500,000$ and standard deviation $100,000.$ The demands during different years are assumed to be independent.

We are working with a $5-$year planning horizon. Capacity levels of $300,000,400,000,500,000,600,000$ and $700,000$ are under consideration.