5. Montyville Pizzeria has a clientele of two types, Hungry (H) consumer and Less Hungry (L) consumer, split 50/50. The type 1 Hungry (H) consumer values the first pizza at $7 and second at $4. The type 2 Less hungry (L) consumer values the first pizza at $6 and second at $2. The cost of production of each pizza is $3. Suppose we want to implement the following: the hungry type buys the 2 pizzas (qu = 2) for a price of PH=11 (for both), and the Less hungry type buys the one pizza (qu = 1) for a price of PL.=6 (for one). Write down the relevant individual rationality and incentive compatibility constraints for all the types (12 points). What are the profit-maximizing prices, payoffs for consumers, and profits for the firm? (18 points)