A Paper Company Dumps Nondegradable Waste into a River That

A paper company dumps nondegradable waste into a river that flows by the firm's plant. The firm estimates its production function to be:
Q = 6KW,
where Q = annual paper production measured in pounds, K = machine hours of capital, and W = gallons of polluted water dumped into the river per year. The marginal products of capital and labor are given as follows:
MP_K = 6W MP_W = 6K
The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year.
a. Determine the firm's optimal ratio of waste water to capital.
b. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce?
c. The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm's cost as a result of the effluent fee?