Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $2,000 per month.Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(10x  x²) .If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁.If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

A) X₁  8 and X₂  8.
B) X₁  4 and X₂  2.
C) X₁  8 and X₂  4.
D) X₁  12 and X₂  8.
E) None of the above.

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Alyssa Darbonne · Accepted Answer

Final Answer : C, Explanation :  To find the number of boats that enter without regulation, set the revenue equal to the cost:$1000(10x-8) = $200010x - 8 = 210x = 10x = 1Therefore, X 1  = 1.To find the number of boats that operate in the bay to maximize total profit, take the derivative of the revenue function with respect to x:d/dx ($1000(10x-4-x^2)) = 10000 - 2000xSet this equal to zero and solve for x:10000 - 2000x = 0x = 5Therefore, X 2  = 5.The correct choice is C, as X 1  = 1 and X 2  = 5.

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