2. A paper company dumps wastewater into a river that flows by the firm’s plant. The firm estimates its production function to be: Q = 6KW Q = pounds of paper produced K = machine hours of capital W = gallons of water dumped. The marginal products of capital and waste are as follows: MPK = 6W MPW = 6K Without regulation, it costs the firm $7.50 to dump a gallon of water and $30/hour to run one of their machines. The firms operating budget is $300,000 per year. a. Find the optimal ratio of waste water to machine hours. b. Given the firm’s budget, how many machine hours and wastewater should the firm use? How much paper will it produce at these levels? c. What are the marginal products and average products of dumping a gallon of water at this level? Assuming that machine hours are fixed in the short run, what is the firms short run marginal cost? d. The state environmental agency decides to impose a $7.50/gallon charge on wastewater effluent. How does this change the firm’s production?