please show work and explain.

5. (20 points) The Old Men and the Sea: Suppose there are 100 old fishermen who are equally skilled, and each of them can catch 5 fish per day by hand. The total output is 500 fish per day. One day, a boat is discovered and the productivity of the boat depends on the number of people on board as follows: Number of people on Total fish caught for the board boat per day 0 0 1 6 2 18 3 32 4 42 5 46 6 40 7 35 8 20 If a fisherman works on the boat, then he cannot catch fish by hand that day. Let's also assume that catching fish in either way is equally exhausting. Discuss how many fishermen will work on the boat and how much fish will be caught in total under two different assumptions. a) The boat is owned by one of the 100 fishermen, and he hires other fishermen for a wage to work for him. b) The boat is not owned by anyone and any fisherman can get on it, and the product will be split equally by all those on board