In Exercises 15 through 19, the demand and supply functions, D(q) and S(q), for a particular commodity are given. Specifically, q units of the commodity will be demanded (sold) at a price of p = D(q) dollars per unit, while q units will be supplied by producers when the price is p = S(q) dollars per unit. In each case:

(a) Find the equilibrium price p_e (where supply equals demand).

(b) Find the consumers’ surplus and the producers’ surplus at equilibrium.

D(q) = −0.3q² + 70; S(q) = 0.1q² + q + 20