The picturesque village of horsehead, massachusetts lies on a bay inhabited by the delectable crustacean, homarus americanus, also known as the lobster. the town council of horsehead issues permits to trap lobsters and is trying to determine how many permits to issue. the economics of the situation is this: 1. it costs $2,000 dollars a month to operate a lobster boat.2. if there are x boats operating in horsehead bay, the total revenue per month from the lobster catch will be f (x) = $1, 000(10x ‑ ) in the graph below, plot the curves for the average product, ap(x) = f (x)/x, and the marginal product, mp(x) = 10, 000 ‑ 2, 000x. in the same graph, plot the line indicating the cost of operating a boat.(b) if permits are free of charge, how many boats will trap lobsters in horsehead, massachusetts? (hint: how many boats must enter before there are zero profits? ) ) what number of boats maximizes total profit? ) if horsehead, massachusetts wants to restrict the number of boats to that maximizing total profit, how much should it charge per month for a lobstering permit? (hint: with a license fee of f thousand dollars per month, the marginal cost of operating a boat for a month would be (2 + f) thousand dollars per month.)