Question 47
A fly farm contains $100001$ fruit flies. A research group wishes to buy some flies from the farm to perform (once) either experiment A or experiment B (but not both).
For experiment A, the research group needs a set of flies in which no fly is a descendant of any other. For such a set, the research group would pay the farm $505$ euros plus $5$ euros per fly bought.
For experiment B, the research group needs a set of flies in which among every two flies, one is a descendant of the other. For such a set, the research group would pay the farm $1000$ euros plus $10$ euros per fly bought.
Prove that there exists a set of flies in the farm for which the research group would pay at least $3010$ euros.
For experiment A, the research group needs a set of flies in which no fly is a descendant of any other. For such a set, the research group would pay the farm $505$ euros plus $5$ euros per fly bought.
For experiment B, the research group needs a set of flies in which among every two flies, one is a descendant of the other. For such a set, the research group would pay the farm $1000$ euros plus $10$ euros per fly bought.
Prove that there exists a set of flies in the farm for which the research group would pay at least $3010$ euros.