Continuous version of the investment model with adjustment costs: the problem that the company faces is how to maximize its objective function in a continuous time horizon: Max n = Loamrt) [310(th It came: subject to if: 2 It k(0):given, k(T):free, T:free Where: - Profit of the industry based on the aggregate capital stock HUQ) - Capital stock of the representative firm of the industry it: - Investment it - investment user cost (70;) Work the foliowing: a) identify state and control variable, properly support your answer. in} Find the optimal path ofthe co-state, control and state variable. c) l evaluated the transversality conditions. d} Develop qualitative solution. e} Graph and explain your results according to macroeconomic theory. Note: make the assumptions that you think are appropriate to obtain your answers