Manufacturing Profit: Rafael estimates that it costs $14 to produce each unit of a particular commodity that sells for $23 per units. There is also a fixed cost of $1200.

a. Express the cost C(x), the revenue R(x), and the profit P(x) as functions of the number of units x that are produced and sold.

b. How much profit is generated when x=2000, x=100. What is the smallest number of units that must be produced for Rafael's company to be profitable?

c. What is the average profit function AP(x)? What is the average profit when 2,500 units are produced?