A manufacturer estimates that each unit of a particular commodity can be sold for $3 more than it costs to produce. There is also a fixed cost of $17,000 associated with the production of the commodity.

a. Express total profit P(x) as a function of the level of production x.

b. How much profit (or loss) is generated when x = 5,000 units are produced? When x = 20,000? What is the smallest number of units that must be sold for production to be profitable?

c. Find the average profit function AP(x). What is the average profit when 10,000 units are produced?