Suppose the market is monopoly by a single firm with the following production function: f(x1,x2)=(αx1rho+(1−α)x2rho)rho1, where x1 and x2 are inputs. And the inverse demand is given as p(Q)=10−2Q. a) (3 points) Setup the cost minimization for the firm. Denote the price of each input as w1 and w2. b) (7 points) derive the minimized cost function. Now assume w1=w2=1. c) (3 points) Setup the profit maximization problem. d) ( 7 points) Characterize the equilibrium price, quantity, and profit.