Suppose that a political candidate is choosing how many television ads to run during his or her campaign. If the candidate runs a 0 ads, he or she will receive v(a) votes, defined as follows:

v(a) = 5750 + 100 ln(a) 500a,

where the parameter > 0 is known by the candidate. The candidate's utility function is linear in the votes he or she receives:

u(v) = v.

(a) What is the optimal number of ads? (That is, what choice of a maximizes u(v(a))?)

(b) Suppose that the candidate does not know , but instead believes that Uniform[0, T], where T > 0 is known by the candidate. What is the optimal number of ads?

(c) Suppose that the candidate does not know , but instead believes that is distributed according to a probability distribution with cumulative distribution function F R+ [0, 1] with known mean > 0. What is the optimal number of ads?