A manufacturing company that produces tires has the following production function and marginal product function

The machine that molds the tires costs $100. Each unit of raw rubber cost the firm $3. The firm sales each tire at a price of $50. The production process produces a waste that is dumped into a nearby river which kills fish. Because of the smaller fish population, this financially harms local fishermen. More specifically, for every unit of raw rubber the tire manufactory uses it reduces the profits of local fishermen by two dollars.

1. Solve for the profit maximizing level of L. Does it correspond to the optimal value on your graph in problem a?
2. What is the profitwhenis used?
3. Solve for the socially optimal level of production. Does it correspond to the socially optimal production level on the graph you constructed in part d?
4. How do the net social benefits differ between the profit maximizing level of productionand the socially optimal level of production. (Hint: Net social benefits are given by)
5. How large should the tax be to incentivize the tire manufacture to produce at the socially optimal level?

Answer all subparts 1,2,3,4,5.