Bavarian Crystal Works designs and produces lead crystal wine decanters for export to international markets. The production manager of Bavarian Crystal Works estimates total and marginal production costs to be TC = 10,000 + 40Q + 0.0025Q2 and MC = 40 + 0.005Q where costs are measured in U. S. dollars and Q is the number of wine decanters produced annually. Because Bavarian Crystal Works is only one of many crystal producers in the world market, it can sell as many of the decanters as it wishes for $50 apiece. Total and marginal revenue are TR = 50Q and MR = 50 where revenues are measured in U. S. dollars and Q is annual decanter production.

a. What is the optimal level of production of wine decanters? What is the marginal revenue from the last wine decanter sold?

b. What are the total revenue, total cost, and net benefit (profit) from selling the optimal number of wine decanters?

c. Is the optimal profit in answer b good enough to keep Bavarian Crystal Works in the market? Please comment on it.