The following table represents the (inverse) demand functions of the three potential clients for a monopolist producer of water with constant marginal cost of $3. GALLONS ANNE BOB CARLA 1 $15 $9 2 $12 $8 $13 $18 3 $11 $7 $11 4 $7 $5 $10 5 $5 $4 $9 6 $2 $3 $5 7 $1 $2 $4 a) Compute the optimal linear price for this monopolist. Also, compute profits, consumer surplus, and deadweight loss with that solution. b) Suppose the monopolist can use a two-part tariff (with variable part a=3). What is the optimal such tariff? Again, compute profits, consumer surplus, and deadweight loss. c) Suppose the monopolist could distinguish students (Bob) from non-students (the other two) and can charge different linear prices to each type of consumer. Compute these optimal linear prices, profits, consumer surplus, and deadweight loss