SoS (Sounds of Silence, Inc) prepares to launch a revolutionary system of bluetooth-enabled noise-cancellation headphones. It is estimated that about 800,000 consumers would be willing to pay $500 for the headphones; an additional 1,000,000 consumers would be willing to pay $250 for the headphones. Though SoS knows this marketing information, it cannot identify a consumer as belonging to one group of the other. SoS is considering the launch of a stripped-down version of the headphones (the strippeddown version uses wires instead of bluetooth). The 800,000 high-valuation consumers would only be willing to pay $325 for the stripped-down version. The remaining 1,000,000 consumers do not particularly care about bluetooth vs. wire connections; they are willing to pay the same $250 for either version. Both the bluetooth version and the stripped-down version cost the same to produce: $100 per unit. 1 (3) (3 points) Suppose that SoS only sells bluetooth-enabled headphones. What is the optimal price? And, what is the profit under the optimal pricing policy? (4) (3 points) Suppose that SoS sells both versions and wants to charge different prices for different versions. What is the highest price of the bluetooth version for the high-valuation buyers? (5) (2 points) What is the total profit under the pricing strategy of question (4)?