A monopolist sells bottles of mineral water to two customers: the high demand customer's demand is described by _h= 3802_h, and the low demand customer's demand is described by _l=150_l. The total willingness to pay of a consumer forunits is the area under their inverse demand curve tillunits. The marginal cost of production is 0. Suppose the monopolist cannot distinguish between the two consumers.

(a)The monopolist is thinking about offering each of the customers two options:

(1) buy_x= 380bottles for a total payment of$, or

(2) buy_y= 150bottles for a total payment of$.

Whatandshould the monopolist set? Show your work.

(b)Suppose the monopolist hadmany customers, of which, a fractionwere the high demand type, and1 - were the low demand type. What is the smallestfor which the monopolist would only offer a 380-bottle package (at a suitably chosen price, not necessarily)? Show your work.