A soft drink company determines that the demand function for one brand of is sport drink is given by: x= D(p) = 12 + p - p2 where p is the price, in dollars, of a sport drink bottle, and x is in hundreds of bottles sold each month. a. Find the elasticity of demand function E(p). b. Find the elasticity at a price of $2 per bottle, stating whether the demand is elastic or inelastic at that price. c. Find the elasticity at a price of $2.50 per bottle, stating whether the demand is elastic or inelastic at that price. At a price of $2.50 per bottle, will a small increase in price cause the total revenue to increase or decrease? d. Find the price of a sport drink bottle at which the revenue will be greatest. (You will need the quadratic formula to solve.) e. What quantity (how many) of bottles will the company sell each month at this price that maximizes revenue