In question 19, since I.M. Hogg is risk neutral, this implies that his objective is to determine the number of negative campaign ads which will maximize the *expected* *number* of voters. The number of negative campaign ads is represented by *n*, where *n *is an integer value ranging from 0 to 4.

In order to solve this problem, the first step involves setting up an equation for the expected number of voters (*E*(*voters*)). One hundred percent of the time, I.M. Hogg gets 500,000 votes; this represents his “core” base of voters. The probability that the ads backfire is 0.2*n*, in which case he fails to obtain any more votes beyond his base of 500,000 voters. However, the probability that the ads don’t backfire is 1-0.*2n*, in which case he gets an additional 100,000 + 40,*000n* votes (over and above his base of 500,000 voters). Anyway, once you have your equation for *E*(*voters*), you can maximize it by differentiating it with respect to *n*, setting the resulting equation equal to 0, and solving for *n*. Since *n* will not likely be an integer, simply round it to the nearest integer value.