The demand for a certain commodity is D(x) = −50x + 800; that is, x units of the commodity will be demanded by consumers when the price is p = D(x) dollars per unit. Total consumer expenditure E(x) is the amount of money consumers pay to buy x units of the commodity.

a. Express consumer expenditure as a function of x, and sketch the graph of E(x).

b. Use the graph in part (a) to determine the level of production x at which consumer expenditure is largest. What price p corresponds to maximum consumer expenditure?