Martin, from Problem 10, now has the opportunity to buy any fractional share, S, of the Yankees t-shirt business. For example, if S = 0.5, he pays $400 for the business, which provides him with a net gain of $200 if the Yankees win and a net loss of $200 if they lose. Assume that Martin starts out with $1000. We can represent his preferences with an expected utility function, with the benefit function W(X) = 3000 X - X2 (for X up to 1500), where X measures dollars.
a. Write a formula for his expected utility as a function of the share purchased.
b. What fraction of the business should he purchase?