document.write( "Question 1194341: For a certain company, the cost for producing x items is 35x+300 and the revenue for selling x items is 75x−0.5x2 .\r
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\n" ); document.write( "\n" ); document.write( "The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!\r
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\n" ); document.write( "\n" ); document.write( "Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)\r
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\n" ); document.write( "\n" ); document.write( "Part b: Find two values of x that will create a profit of $300 .\r
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\n" ); document.write( "\n" ); document.write( "The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).
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Algebra.Com's Answer #826541 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

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\n" ); document.write( "\n" ); document.write( "Profit = Revenue - Cost
\n" ); document.write( "P(x) = R(x) - C(x)
\n" ); document.write( "P(x) = (75x-0.5x^2) - (35x+300)
\n" ); document.write( "P(x) = 75x-0.5x^2 - 35x-300
\n" ); document.write( "P(x) = -0.5x^2 + 40x - 300\r
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\n" ); document.write( "\n" ); document.write( "The profit expression is -0.5x^2 + 40x - 300\r
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\n" ); document.write( "\n" ); document.write( "Part (b)\r
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\n" ); document.write( "\n" ); document.write( "Set the profit expression equal to 300 and solve for x.\r
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\n" ); document.write( "\n" ); document.write( "-0.5x^2 + 40x - 300 = 300
\n" ); document.write( "-0.5x^2 + 40x - 300 - 300 = 0
\n" ); document.write( "-0.5x^2 + 40x - 600 = 0
\n" ); document.write( "Factoring may be possible, but I prefer to use the quadratic formula.\r
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\n" ); document.write( "\n" ); document.write( "Plug in a = -0.5, b = 40, c = -600
\n" ); document.write( "\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%2840%29%2B-sqrt%28%2840%29%5E2-4%28-0.5%29%28-600%29%29%29%2F%282%28-0.5%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-40+%2B-+sqrt%28400%29%29%2F%28-1%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-40%2B-+20%29%2F%28-1%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-40%2B20%29%2F%28-1%29\" or \"x+=+%28-40-20%29%2F%28-1%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-20%29%2F%28-1%29\" or \"x+=+%28-60%29%2F%28-1%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+20\" or \"x+=+60\"\r
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\n" ); document.write( "\n" ); document.write( "Another approach you can take is to graph these two equations
\n" ); document.write( "y = -0.5x^2 + 40x - 300
\n" ); document.write( "y = 300
\n" ); document.write( "using a tool like Desmos
\n" ); document.write( "https://www.desmos.com/calculator/jfde1smu5r
\n" ); document.write( "In the link above, the graph is shown. The points of intersection will give us the x solutions. Ignore the y coordinates of each point.
\n" ); document.write( "You can click on the intersection point to have the coordinates show up.
\n" ); document.write( "The intersections of (20,300) and (60,300) lead to the solutions found earlier (x = 20 and x = 60).\r
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\n" ); document.write( "\n" ); document.write( "Interpretation: If the company sells either 20 items or 60 items, then they will have a profit of $300.
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