Consider the case of a rm that produces output it [sold at price p} using a production function x = A'ka'e. where i is labor, k is capital, and e is energy (for example, oil or electricity). The cost of each energy unit is ca. a} what is the interpretation of A in the production function? b} Set up the prot maximization problem for the rm. cl 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 of: if you don't go through all the algebra] e1 Find the optimal supply function for x. f :I Set up the cost minimization problem. Show the relevant Technical Rates of Substitution