A movie theater is trying to figure out how to price small and large popcorns. After some market research, it discovers that people either go to the movie theater alone as an individual, or together as a couple. Individuals are willing to pay $6 for a small popcorn, or $7 for a large popcorn. Couples are willing to pay $8 for a small, or $12 for a large. (Individuals and couples each buy at most a single popcorn.) Popcorn has a negligible marginal cost to the theater, which we can approximate as 0. The theater can set prices for large and small popcorns, but can't directly charge different prices to individuals and couples. (a) The theater decides it will try to sell large popcorns to couples, but it isn't sure what size popcorn (if any) to sell to individuals. i. If the theater wants to sell large popcorns to both individuals and to couples, what would be the profit-maximizing price for large popcorn? ii. If the theater wants to sell small popcorns to individuals and large popcorns to couples, what would be the profit-maximizing prices? iii. If the theater wants to sell large popcorns to couples and nothing to individ- uals, what would be the profit-maximizing prices