SOLUTION: A company's profit, in thousands of dollars, on sales of computers is modelled by the function P(x)= -2(x-3)^2+ 50, where x is in thousands of dollars, on sales of computers sold.

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Question 284169: A company's profit, in thousands of dollars, on sales of computers is modelled by the function P(x)= -2(x-3)^2+ 50, where x is in thousands of dollars, on sales of computers sold. The company's profit, in thousands of dollars, on sales of stereo systems is modelled by the function P(x) = -(x-2)(x-7), where x is in thousands of stereo sytems sold. Calculate the maximum profit the business can earn.
Answer by stanbon(75887) About Me  (Show Source):
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A company's profit, in thousands of dollars, on sales of computers is modeled by the function P(x)= -2(x-3)^2+ 50, where x is in thousands of dollars, on sales of computers sold. The company's profit, in thousands of dollars, on sales of stereo systems is modeled by the function P(x) = -(x-2)(x-7), where x is in thousands of stereo sytems sold. Calculate the maximum profit the business can earn.
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Max profit on sales of computers: Vertex is (3,50) so max = $50K
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Max profit on sales of stereos:
P(x) = -[x^2-9x+14]
P(x) = -x^2+9x-14
a = -1 ; b = -9
Max occurs at x = -b/2a = -9/(-2) = 4.5
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Profit when x = 4.5
P(4.5) = -(4.5-2)(4.5-7)
P(4.5) = -(2.5)(-2.5) = $6.25K
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Total Max Profit: 50K + 6.25K = $56.25K
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Cheers,
Stan H.