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Answer :
Final answer:
The correct profit function from the options provided is Option A, which is represented by the polynomial equation p(x) = 1200x - 80x^2 - x^3 - 48,000. This function fits the typical shape of a profit curve where the profit increases initially and then decreases as production quantity x increases.
Explanation:
The profit function for a product as given in the question can be verified by careful reading. There seems to be a small typo in the original equation; however, we can determine the correct profit function by looking at the options provided. The correct profit function should be a polynomial where the signs of the terms affect the overall shape of the profit function graph.
Among the options, the correct profit function appears to be the one that decreases the profit as x increases beyond a certain point due to the negative cubic term that will dominate at high levels of x. We can exclude options with incorrect signs in front of the numbers, as they would not mathematically match the typical form of a profit curve. So, the correct profit function in this case is:
Option A: p(x) = 1200x - 80x^2 - x^3 - 48,000
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