Q3. Vanna Boogie likes to have large parties. She also has a strong preference for having exactly as many men as women at her parties. In fact, Vanna's preferences among parties can be represented by the utility function $U(x, y) = \text{min}\{2x - y, 2y - x\}$ where $x$ is the number of women and $y$ is the number of men at the party. Suppose indifference curve shows utility of 10.
(1) What point on this curve gives Vanna a utility of 10?
(2) If Vanna has 16 women at her party and more men than women, and if she thinks the party is exactly as good as having 10 men and 10 women, how many men does she have at the party?
(3) If Vanna has 16 women at her party and more women than men, and if she thinks the party is exactly as good as having 10 men and 10 women, how many men does she have at her party?
