A manufacturer of machinery parts determines that q units of a particular piece will be sold when the price is p=170−q dollars per unit. The total cost of producing those q units is C(q) dollars, where C(q)=q^3−35q^2+4q+7000
(a) How much profit is derived from the sale of the q units at p dollar per unit? (b) For what value of q is profit maximized? Round to the nearest whole number. (c) Find the consumers' surplus for the level of production q0 that corresponds to maximum profit.