1.Suppose the price p(t) of a particular commodity varies in such a way that its rate of change with respect to time is proportional to the shortage D - S, where D(p) and S(p) are the demand and supply functions for the commodity, respectively.

a)Find p(t) for the case where andS(p) = 5 + 4p, if the price is $4 when t = 0 and is $3 when t = 5.

b)Calculate both the consumer's surplus and the producer's surplus, where the market equilibrium exists.