Princess Buttercup has a multitude of potential suitors. She wishes to separate them into two groups - those who are truly interested in her hand in marriage, and those who are only interested because she's convenient, pretty, and rich. Let's call these two groups "interested" and "nonchalant," respectively. In an attempt to separate the two groups, Princess Buttercup devises a plan under which potential suitors must slay dragons before coming to the castle to court her.
• Those who slay the requisite number of dragons, , will be allowed to court her.
• Those who do not slay the requisite number of dragons will only be allowed to court Buttercup's ugly half-sister, Princess Poison Ivy.
• To a member of either group, the benefit to courting Princess Buttercup is equal to $1,000.
• To a member of either group, the benefit to courting Princess Poison Ivy is $64.
• To a member of the "interested" group, who pursue their goal with unbridled passion, the cost of passing Buttercup's test is given as D2, where D is the number of dragons slain.
• To a member of the "nonchalant" group, who pursue their goal halfheartedly, the cost of passing Buttercup's test is given as D3, where D is the number of dragons slain.
a. Princess Buttercup wants to sort the interested suitors from the nonchalant suitors. What is the minimum number of dragons Princess Buttercup can ask potential suitors to slay if she wants them to separate into groups? You can round to an appropriate integer.
b. Suppose that Princess Buttercup asks suitors to slay three fewer dragons than you indicated in your answer to (a). Why will ask suitors to slay this many dragons not help Princess Buttercup filter out the nonchalant suitors?
c. What is the maximum number of dragons Princess Buttercup can ask potential suitors to slay if she wants to be able to distinguish between interested and nonchalant suitors? (Again, you may round your answer to an appropriate integer.)
d. Suppose that Princess Buttercup asks potential suitors to slay three more dragons than you indicated in your answer to (c). Why will asking suitors to slay this many dragons not help Princess Buttercup filter out the nonchalant suitors?
e. Suppose that Princess Buttercup has appropriately set the number of dragons, filtered out the nonchalant suitors, and from the pool of interested suitors chosen her prince. Now, she wishes to see if her prince wants her because of love, or whether her prince is only interested given her vast fortune. What modern American legal device might Princess Buttercup use as a screening tactic to discover the true answer? Explain your response.