A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^(2)+12 What sock price should the company set to earn a maximum profit? dollars

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A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by:  P(x)=-3(x-5)^(2)+12 What sock price should the company set to earn a maximum profit? dollars

Bytelearn · Accepted Answer

Identify Function Type: Identify the type of function given for the profit P(x). The function P(x) = -3(x-5)² + 12 is a quadratic function in the form of P(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.Determine Parabola Vertex: Determine the vertex of the parabola. Since the coefficient of the squared term is negative (-3), the parabola opens downwards, which means the vertex represents the maximum point on the graph. The vertex (h, k) can be found directly from the equation P(x) = -3(x-5)² + 12, which gives h = 5 and k = 12.Find Sock Price: Find the sock price for maximum profit. The sock price that corresponds to the maximum profit is the x-value of the vertex, which is h = 5 dollars.Check Result: Check the result. Since the parabola opens downwards and the vertex is the highest point, the sock price of $5 will indeed give the maximum profit according to the model.

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