Bavarian Crystal Works designs and produces lead crystal wine decanters for export to international markets. The production manager of Bavarian Crystal Works estimates total production cost and total benefit to be:

 TC = 10,000 + 40Q + 0.0025Q², TB = 70Q     

Where total cost and total benefit are measured in U.S dollars and Q is annual decanter production. Because Bavarian Crystal Works is the only one of many crystal producers in the world market, it can sell as many of decanters as it wishes for $70 apiece.

a) What is the optimal level of production of wine decanters?

b) Verify that this level of output maximizes not minimizes profit

c) At the optimal level of production of decanters, an extra decanter can be sold for $70, thereby increasing total revenue by $70. Why does the manager of this firm not produce and sell one unit more?