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Problem: 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 payo 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.
Required:
Question 1: What is the minimum wait time, m, that will achieve separation of types?
Question 2: After a while the charity finds that it can successfully identify and turn away college students half of the time. College students who are turned away receive no free meal and also incur a cost of 5 for their time and embarrassment. Will the ability to partially identify college students reduce or increase the answer above? Explain.
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