On a tropical island there are 100 potential boat builders, numbered 1 through 100. Each can build up to 16 boats a year, but anyone who goes into the boat-building business has to pay a fixed cost of $15. Marginal costs differ from person to person. Where y denotes the number of boats built per year, boat builder 1 has a total cost function c₁(y) = 15 + y. Boat builder 2 has a total cost function c₂(y) = 15 + 2y, and more generally, for each i, from 1 to 100, boat builder i has a cost function c_i(y) = 15 + iy. If the price of boats is 40, how many boats will be built per year?