A quadratic revenue function often occurs in practice. The reason is that as more units are produced, the price must be lowered in order to sell them all.

a) A company has found that if they produce x units of a product, they must sell them each at $10 - 0.2x if they are to sell all of them. Determine the revenue function.

b) Their fixed costs are $40 and their variable costs per unit are $1. Determine the cost and profit functions.

c) Graph all three functions (on the same graph) over an appropriate range.