1. A team of three (Hongjin, Ioannis, Jamal) is working on a project that requires at least eighty hours of work to complete, but if they work one-hundred hours they will win the Teamworkaholic award, which involves a $10,000 cash award to each. Each has forty hours available. They could use half of their time to take a new training course instead, which is called "Leadership Academy." The team isn't sure how interested everyone is in the "Leadership Academy" - except, Ioannis has already completed a pilot of it. So it has a value of $0.for him..Hongjin claims that the value of the "Leadership Academy" to her, personally, is $15,000. The team isn't sure whether Hongjin values the "Leadership Academy" at $5,000 or $15,000. Jamal would very much like to participate in the "Leadership Academy" and the value to him would be $12,000. Except for any missed training opportunities, no one incurs a cost from working additional hours. (i) How many people, at most, could take the Leadership Academy while still allowing the team to finish the project? (I.e. work eighty hours overall.). (ii) How many people, at most, could take the Leadership Academy while enabling the team to win the Teamworkaholic award? (I.e. work one hundred hours overall.) (iii) If the team's goal is only to complete the project, who should work how much in order to maximize value for the group? (Does it depend on Hongjin's possible valuations of the training? If so, how?) (iv) If the team's goal is to win the award, who should work how much in order to maximize value for the group? (Does it depend on Hongjin's possible valuations of the training? If so, how?) (v) Design a VCG mechanism which allows the team to arrange work hours to win the award in the most efficient way. (Hint: This will be a payment someone has to make depending on what everyone claims their value for the training to be. The payment will incentivize Hongjin to be honest about the value of the training to her.)