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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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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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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document.write( "Part b: Find two values of x that will create a profit of $300 .\r
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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). \n" );
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Algebra.Com's Answer #826541 by math_tutor2020(3817)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Part (a)\r \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The profit expression is -0.5x^2 + 40x - 300\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "=====================================================\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Part (b)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Set the profit expression equal to 300 and solve for x.\r \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Plug in a = -0.5, b = 40, c = -600 \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \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. \n" ); document.write( " \n" ); document.write( " |