$.$ Individual Problems $14-6$

At a student caf$,$ there are equal numbers of two types of customers with the following values. The caf$$ owner cannot distinguish between the two types of students because many students without early classes arrive early anyway $($i$.$e$.,$ she cannot price$-$discriminate$).$

Students with Early Classes

Students without Early Classes

Coffee$6757$Banana$4696$

The marginal cost of coffee is $5$ and the marginal cost of a banana is $20.$

The caf$$ owner is considering three pricing strategies:

$1.$Mixed bundling: Price bundle of coffee and a banana for $153,$ or just a coffee for $67\mathrm{.}2.$Price separately: Offer coffee at $57,$ price a banana at $96\mathrm{.}3.$Bundle only: Coffee and a banana for $113.$ Do not offer goods separately.

Assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle.

For simplicity, assume there is just one student with an early class, and one student without an early class.