document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037039>Question 1037039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company’s manager estimated that the cost C, in dollars, of producing n items is C equals 7 n plus 350. The company sells each item for $12. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #651770 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=651770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's see if we can find the right equation for this.\r<BR>\n" );
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document.write( "cost = 7 * number of units plus 350.\r<BR>\n" );
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document.write( "if we let c = the cost and n = the number of units, then the formula becomes c = 7*n + 350.\r<BR>\n" );
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document.write( "revenue - 12 * number of units.\r<BR>\n" );
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document.write( "if we let r - the revenue and n = the number of units, then the formula becomes r = 12 * n.\r<BR>\n" );
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document.write( "profit = revenue minus cost.\r<BR>\n" );
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document.write( "if we let p = profit and r = revenue and c = cost, then the formula becomes p = r - c.\r<BR>\n" );
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document.write( "we have 3 formulas:\r<BR>\n" );
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document.write( "c = 7 * n + 350 = cost formula.<BR>\n" );
document.write( "r = 12 * n = revenue formula.<BR>\n" );
document.write( "p = r - c = profit formula.\r<BR>\n" );
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document.write( "since we know that c = 7 * n + 350 and r = 12 * n, then we can substitute in the profit formula to get:\r<BR>\n" );
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document.write( "p = r - c becomes p = 12 * n - (7 * n + 350).\r<BR>\n" );
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document.write( "simplify this to get p = 12 * n - 7 * n - 350.\r<BR>\n" );
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document.write( "combine like terms to get p = 5 * n - 350.\r<BR>\n" );
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document.write( "in order for the company to make a profit, p has to be greater than 0.\r<BR>\n" );
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document.write( "the formula for profit becomes p > 0.\r<BR>\n" );
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document.write( "since p = 5 * n - 350, then you get 5 * n - 350 > 0.\r<BR>\n" );
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document.write( "solve for n in this formula to get n > 350 / 5 becomes n > 70.\r<BR>\n" );
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document.write( "the number of units sold has to be greater than 70 in order for the company to make a profit.\r<BR>\n" );
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document.write( "let's see what happens to each of these formulas.\r<BR>\n" );
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document.write( "if 70 units are sold, then you get.\r<BR>\n" );
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document.write( "cost = 7 * 70 + 350 = 840<BR>\n" );
document.write( "revenue = 12 * 70 = 840<BR>\n" );
document.write( "profit = revenue minus cost = 840 - 840 = 0.\r<BR>\n" );
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document.write( "0 profit is made when 70 units are sold.\r<BR>\n" );
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document.write( "you can see that, when less than 70 units are sold, the profit is negative which means the company takes a loss.\r<BR>\n" );
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document.write( "you can see that, when more than 70 units are sold, the profit is positive which means the company makes a profit.\r<BR>\n" );
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document.write( "based on the given equations, the break even point is 70 units.\r<BR>\n" );
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document.write( "the company makes a profit when more than 70 units are sold.\r<BR>\n" );
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document.write( "this can also be shown graphically.\r<BR>\n" );
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document.write( "you can graph the revenue equation and the cost equation and see that the revenue equation becomes greater than the cost equation when x is greater than 70.\r<BR>\n" );
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document.write( "that graph is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/060403.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can also graph the revenue equation minus the cost equation and see that the profit becomes greater than 0 when x is greater than 70.\r<BR>\n" );
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document.write( "that graph is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/060404.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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