Question
A company's profit is modeled by the function P(x) = -2x^2 + 100x - 800, where x is the number of items sold. Find the number of items sold when the profit is maximized.
A company's profit is modeled by the function P(x) = -2x^2 + 100x - 800, where x is the number of items sold. Find the number of items sold when the profit is maximized.
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To find the number of items sold when the profit is maximized, we need to determine the vertex of the quadratic function.
The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula:
x = -b/(2a)
In this case, P(x) = -2x^2 + 100x - 800, so a = -2, b = 100, and c = -800.
Using the formula, the x-coordinate of the vertex is:
x = -100/(2*(-2))
x = -100/(-4)
x = 25
Therefore, the number of items sold when the profit is maximized is 25.
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