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 = 8KW, where Q = annual paper production measured in pounds, of capital, and of polluted water dumped into the river per year. The marginal products of capital (MPK) and labor (MPW) are given as follows: MPK = 8W MPW = 8K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $10 per gallon dumped. The firm estimates a $40 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 $10 effluent fee for each gallon that isdumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ?