Happy, Grumpy, Dopey, Sleepy, Sneezy, Doc, and Bashful are miners, who have nothing to do with their time but to go mining. There are no other miners in the vicinity. Each miner can dig in either of two mines. The number of gold nuggets that a miner can find in a day depends both on which mine he is working and how many other miners are present in that mine, as indicated by the following chart: a. If entry to the mines is free, how many miners work in each mine? b. At the social optimum, how many miners would work in each mine? c. What system of entry fees to the mines could bring about that social optimum? d. Suppose that both mines are owned by a wicked queen who can set entry fees. What fees would she set