Suppose D(q)=1300−q^2 and S(q)=(1/4)q^2+40q+0 are the demand and supply functions for a particular commodity. That is, q thousand units of the commodity will be demanded (sold) at a price of p=D(q) dollars per unit, while q thousand units will be supplied by producers when the price is p=S(q) dollars per unit.
a. Find the equilibrium price p0 where supply equals demand. Dollars per unit
b. Compute the consumers' surplus at equilibrium. In dollars
c. Compute the producers' surplus at equilibrium. In dollars