A firm produces two kinds of products: Word and Excel. Both products are made by a monopolist. Four consumers are considering buying these products. The first consumer's willingness-to-pay (WTP) for Word is 10, and her WTP for Excel is 1. The second consumer's WTP for Word is 8, and her WTP for Excel is 5. The third consumer's WTP for Word is 5, and her WTP for Excel is 8. Lastly, the fourth consumer's WTP for Word is 1, and her WTP for Excel is 10. Assume that marginal costs for both products are zero.

(1) (10 point) Suppose that both products need to be sold separately. What should be the optimal price for each product? Also, compute the firm's profit under the optimal a la carte pricing.

(2) (5 point) Now suppose that bundling is the only option. In other words, the monopolist only sells two products together. What should be the optimal price for the bundle? Also, compute the firm's profit under the optimal bundling.

(3) (10 point) The firm can use both bundling and a la carte pricing, that is, mixed bundling. What should be the optimal mixed bundling prices? Compute the firm's profit under the optimal mixed bundling as well.