[60 points] Suppose you are in charge of procuring copper supplies for your company's manufacturing process. The net benefit, measured in profits, from a quantity of Q tonnes of copper is 2vQ -M where M is the amount of money paid for the materials. There is only one supplier of copper, Copper Co. You do not know Copper Co.'s cost of production for certain but you know that it has three possible types: C1, C2, or C3 per tonne of copper with ci Q2 > Q: and show that the following three constraints bind: i. individual rationality constraint for the type 3 Copper Co.; ii. incentive compatibility constraint requiring that type 2 prefers C2 over Ca; and ili. incentive compatibility constraint requiring that type 1 prefers Cover C2.(F) Substitute out for AM], J\"; and M1, using expremiom: found in part 2(0) to express your objective function (expemted prom} in terms of (2], Q2 and ()3. (g) 'Write down the firstorder conditions for maximization and solve them for 1.?th and ()3. (Him: the rst order condition sets the derivative of the objective flinc tion with respect to Q], ()2 and Q\" to zero. If fer) = Z then its derivative is HI} = 5;.) (h) Solve for Ml, M2 and 1112