Consider the example of a tied product that was discussed in class. Nespresso is the only seller of its coffee brewing machines and the compatible capsules. The cost of producing each machine is 5, and capsule production costs are 2 per capsule. There are two types of potential customers, high demand (H) and low (L). Their respective demands for the number of coffee drinks are D(p) = 16 - p for H types, and DL(p) = 12 -p for L types, if they pay a price of p per capsule. There are equal numbers of each customer type, but Nespresso cannot identify a customer's type before they make a sale. (That is, third degree price discrimination is not possible.) (a) Suppose that Nespresso charges p per capsule. Derive the consequent willingness to pay for the brewing machine for each customer type, as a function of p. (b) Suppose that Nespresso sets a price for brewing machines so that L types are just indifferent between buying the machine or not. Express Nespresso's profits as a function of the price p per capsule. Show that these profits are maximized when p = 4. (c) Show that Nespresso could not earn higher profits by selling only to the H types (and setting the optimal prices for machines and capsules in that case).