Suppose that a rm produces two outputs with cost function G where C(q)=q+2q+1o given output levels I; = [(11,132) 2 ll. You could disregard the nonnegativity constraints on q and think of this as an exercise of unconstrained optimization. (a) If the rm took the output prices as given and xed, what would he the protmaximizing solution[s)'? Would the solution be unique? Explain. Now, for the rest of the problem (h) (d), assume that the rm is a monopoly in both of the output markets. The demand functionss for the two outputs, Q1 and Q2, satisfy 91(19): A1 - 2P1 3P2, Q2(P) = A2 5P1 3P2 for all output prices P = (131,132) 2 0, where A1, A2, a, b are positive real numbers and are given exogenously. The rm talces these downwardsloping demand curves when choosing output levels. (h) Find the output levels that satisfy the rstorder condition for maximum prot. (c) Check the secondorder condition. \"That would you conclude from your nding? Is there a unique solution? How would you answer depend on A1,A2, a, b? ((1) Compute the maximum prot level, assuming that the secondorder condition holds for an interior solution