Consider the case of a firm that produces output x (sold at price ,0) using a production function x = A*l\"k1'\"'Bel3, where l is labor, k is capital, and e is energy (for example, oil or electricity). The cost of each energy unit is Ce. a) What is the interpretation ofA in the production function? b) Set up the profit maximization problem for the firm. c) Find the optimality conditions for all the inputs in the production function. d) Find the input demand functions for labor, capital, and energy. [it's ok ifyou don't go through all the algebra] e) Find the optimal supply function for x. f) Set up the cost minimization problem. Show the relevant Technical Rates of Substitution