II. Helping Conchita-Crem to minimize costs Suppose that the labor cost of Conchita-crem is $20 USD per hour, and the cost of capital is $5 USD per hour. Suppose the production function for conchas is q = 10L2K/2 a) José Antonio produces 1000 conchas. He is currently using 100 workers and 100 ovens. Is he optimizing his use of inputs of production? b) What is the rule to optimize the use of inputs of production? c) Find the optimal level of labor and capital for Conchita-Crem. What is its total cost? d) Now suppose that the rental price of ovens for Conchita-Crem increases 100%. Would the production change? What would be now the rule to efficiently use inputs of production? How much labor and capital be used? What is the total cost now? Compare it to your answer in c. e) Find the input demand functions for capital and labor. Remember these functions specify the amount of labor or capital that Conchita-Crem will use as a function of production level q. f) Suppose now that José Antonio would like to know the expansion path of his firm and his long-run cost curve. He wants to know that for up to 5,000 conchas produced. You must use graphs to depict the scenario.