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An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function , where P(x) is the profit in dollars and x is the number of automobiles made and sold.
-What is the maximum profit?

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Use the following to answer questions :
An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function  , where P(x) is the profit in dollars and x is the number of automobiles made and sold.
-What is the maximum profit?

Quizplus · Accepted Answer

Since the function is quadratic, the maximum profit will occur at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.002x + 8 and b = 2400. Simplifying, we get x = -b/2a = -2400/(2*(-0.002x + 8)). Plugging in x = 150 (half of the maximum capacity of 300), we get x = 150, which means the maximum profit occurs when 150 cars are sold. Evaluating the function at x = 150, we get P(150) = $100,000. Therefore, the maximum profit is $100,000, which corresponds to choice C.

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