In a faraway land, 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 vaitors must slay dragons before coming to the castle to court her, Only those who kill the requisite number of dragons, D", 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 Be -100. To a member of either group, the benefit to courting Princess Poison Ivy is By 20 To a member of the "interested"group. who pursue their goal with unbridled passion, the cost of passing Buttercup's best is given as C=20+10D, where Dis the number of dragons slain. To a member of the "nonchalant" group, who pursue their goal half-heartedly, the cost of passing Buttercup's test is given as Cy = 40+20D where D is the number of dragons slain A Princess Buttercup wants to sort the interested suitors from the nonchalant suitors. What is the moumeen number of dragons Princess Buttercup can ask potential suitors to shay if she wants them to separate into groups? You can round to an appropriate integer. B Show that if Princess Buttercup requires suitors to slay $ dragons, only interested suitors will court her C What is the maximion number of dragons Princess Buttercup can ask potential suitors to slay if she wants to be able to distinguish between interested and nonchalant suitors? D 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 ber prince wants her because of love, or whether ber prince is only interested given her vast fortune. What modern legal device might Princess Buttercup use as a screening tactic to discover the true answer? Explain your response