Question

A local charity has been given a grant to serve free meals to the homeless in its community, but it is worried that its program might be exploited by nearby college students who are always interested in a free meal. both a homeless person and a college student receive a payoff of 10 for a free meal. the cost of standing in line for the meal is m2 400 for a homeless person and m2 250 for a college student, where m is the number of minutes spent waiting in line. assume that the staff of the charity cannot observe the true type of people coming for free meals.
a. what is the minimum wait time, m, that will achieve separation of types?

Answer 1

Homeless: 
10 – t^2 /320 > 0
10 > t^2 /320
3200 > t^2 
t < 40√2 = 56.6 
College students: 
10 – t^2 /160 > 0
10 > t^2 /160
1600 > t^2 
t < 40
Wait time would have to be at least 40 minutes to prevent college students from waiting.