My oldest daughter is just about 8 years old. She has told me that she wants to go on a date with a boy in her class (Not going to happen). While humoring her, I asked her why she thinks he would be a good date, and she told me it was because he has a lot of Pokémon. Now, I know a lot about Pokémon and how that translates to date ability. In fact, I know that the effort it takes to catch Pokémon can be expressed as

P^2/0

where p represents the number of Pokémon someone has caught, and 0 represents some private information. 0= 100 for a low quality date (Just a typical Pokémon trainer) whereas 0 = 2311 for a high quality date (a Pokémon master). Furthermore, a date with my daughter has a payoff associated with it of UD = 275 (She is pretty awesome), but not going on a date with my daughter has a payoff of UN = 50. My daughter only likes to date those who are of high quality and would prefer to reject those of either low or unknown quality.

a) How many Pokémon would a high quality date be willing to catch to earn a date with my daughter? (This won't be an integer)

b) How many Pokémon would a low quality date be willing to catch to earn a date with my daughter?

c) How many Pokémon must a high quality date catch in order to effectively signal their type?