In Exercises 30 through 33, supply and demand functions, S(x) and D(x), are given for a particular commodity in terms of the level of production x. In each case:

(a) Find the value of x_e for which equilibrium occurs and the corresponding equilibrium price p_e.

(b) Sketch the graphs of the supply and demand curves, p = S(x) and p = D(x), on the same graph.

(c) For what values of x is there a market shortage? A market surplus?

S(x) = 2x + 7.43 and D(x) = −0.21x² − 0.84x + 50