Question 1162430
The cost is {{{5000+4x+0.001x^2}}}
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The sale price is {{{25x}}}
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Therefore, the profit is {{{25x - (5000+4x+0.001x^2)}}}
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Simplify the profit:
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{{{25x - 5000 - 4x - 0.001x^2}}}
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= {{{-0.001x^2 + 21x - 5000}}}
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To find the maximum profit, use the equation {{{(-b)/2a}}}, where b = 21 and a = -0.001.
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{{{(-b)/2a}}} = {{{(-21)/(2(-0.001))}}} = {{{(-21)/(-0.002)}}} = 10500
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<b>The maximum profit is reached when the manufacturer makes 10,500 blankets.</b>
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Check it:
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When the manufacturer makes 10,500 blankets, the profit is:
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{{{-0.001x^2 + 21x - 5000}}} = {{{-0.001(10500)^2 + 21(10500) - 5000}}} = 105250.
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When the manufacturer makes 10,499 blankets, the profit is:
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{{{-0.001x^2 + 21x - 5000}}} = {{{-0.001(10499)^2 + 21(10499) - 5000}}} = 105249.999
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When the manufacturer makes 10,501 blankets, the profit is:
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{{{-0.001x^2 + 21x - 5000}}} = {{{-0.001(10501)^2 + 21(10501) - 5000}}} = 105249.999