11)Monopolist uses one input X, which she purchases at the fixed price r = 5 to produce her output, Q. Her demand and production functions are p = 85 -3q and q = 2x respectively. Determine the values of p, q, and x at which the monopolist maximizes her profit. Let two duopsonists have production functions q1 = 13x 0.2x1 and q2 = 12x2 0.1x2 where x1, x2 are the input levels employed by the duopsonists. Assume that the input supply function is r = 2 + 0.1(x1 + x2) where r is the supply price of the input, and that q1 and q2 are sold in competitive markets for prices p1 = 2 and p2 = 3. (a) Find the input reaction functions. (b) Determine the Cournot equilibrium values for x1, x2, and q1, q2, 1,2 An entrepreneur is engaged in tree growing. He purchases a seedling for 4 dollars, incurs a cultivation cost flow at a rate of G(t) = 0.4t dollars per year during the life of a tree, and sells the tree at t = T for R(T) = 4 + 8T T2 dollars. The market rate of interest is 0.20. Determine an optimal length for his cultivation period, T. Apply the appropriate second-order condition to verify that your solution is a maximum.