Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $4,000 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(28x - 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 = 24 and X₂ =24. B)X₁ = 28 and X₂ = 16. C)X₁ = 24 and X₂ = 12. D)X₁ = 12 and X₂ = 10. E)None of the above.

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To maximize profits, we need to find the number of lobster boats that will maximize revenue minus costs, i.e., maximize (1000(28x - x^2)) - 4000x. Taking the derivative of this expression with respect to x and setting it to zero, we get: 28000 - 2000x = 0 x = 14 This means that 14 lobster boats will maximize profits. Therefore, X₂ = 14. To find X₁, we need to find the point at which new entrants will no longer make a profit. Setting the revenue equal to costs, we get: 1000(28x - x^2) = 4000x 28000 - 1000x = x^2 x^2 + 1000x - 28000 = 0 Using the quadratic formula, we get: x = 24 or x = -116 Since we can't have negative lobster boats, we only take x = 24. Therefore, X₁ = 24. The only choice that matches these values is C.

Suppose That in Horsehead, Massachusetts, the Cost of Operating a Lobster