document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1015468>Question 1015468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am in straight panic mode and can't figure this out\r<BR>\n" );
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document.write( "The following amounts represent the costs for producing a particular item. Assume the cost function for producing x items is linear. Find the cost function, revenue function, and profit function.\r<BR>\n" );
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document.write( "Fixed Cost      Marginal Cost Per Item    Item Sells For<BR>\n" );
document.write( "15,000		         8.50			45\r<BR>\n" );
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document.write( "What is the cost function C(x)=<BR>\n" );
document.write( "What is the revenue function R(x)=<BR>\n" );
document.write( "What is the profit function? P(x)=<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 #631828 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=631828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> fixed cost is 15,000<BR>\n" );
document.write( "marginal cost per item is 8.50<BR>\n" );
document.write( "sale price per item is 45.\r<BR>\n" );
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document.write( "marginal cost per item appears to me to be the cost per item above and beyond your fixed cost.\r<BR>\n" );
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document.write( "it more than likely includes material plus labor.\r<BR>\n" );
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document.write( "the fixed cost more then likely includes the cost of the machine that produces the item.\r<BR>\n" );
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document.write( "there are also other fixed costs involved such as land and building that are probably not included in this.\r<BR>\n" );
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document.write( "no matter.\r<BR>\n" );
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document.write( "the formulas would be as follows:\r<BR>\n" );
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document.write( "c(x) = fc + vc\r<BR>\n" );
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document.write( "fc is fixed cost<BR>\n" );
document.write( "vc is cost per item sold.<BR>\n" );
document.write( "that's what is called your marginal cost.\r<BR>\n" );
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document.write( "r(x) = vr\r<BR>\n" );
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document.write( "vr is revenue per item sold.\r<BR>\n" );
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document.write( "p(x) = r(x) - c(x)\r<BR>\n" );
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document.write( "this tells you that your profit is equal to your revenue minus your cost.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "fc = 15,000<BR>\n" );
document.write( "vc = 8.50<BR>\n" );
document.write( "rc = 45.00\r<BR>\n" );
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document.write( "your cost formula becomes:\r<BR>\n" );
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document.write( "c(x) = 15,000 + 8.50 * x\r<BR>\n" );
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document.write( "your revenue formula becomes:\r<BR>\n" );
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document.write( "r(x) = 45 * x\r<BR>\n" );
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document.write( "your profit formula becomes:\r<BR>\n" );
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document.write( "p(x) = r(x) - c(x) = 45 * x - (15,000 + 8.50 * x)<BR>\n" );
document.write( "simplify this to get p(x) = 45 * x - 15,000 - 8.50 * x<BR>\n" );
document.write( "simplify further to get p(x) = 36.5 * x - 15,000.\r<BR>\n" );
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document.write( "so you have:\r<BR>\n" );
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document.write( "c(x) = 15,000 + 8.50 * x<BR>\n" );
document.write( "r(x) = 45 * x<BR>\n" );
document.write( "p(x) = r(x) - c(x) = 36.5 * x - 15,000\r<BR>\n" );
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document.write( "your break even point is when r(x) = c(x).\r<BR>\n" );
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document.write( "set c(x) = r(x) and the formula becomes:\r<BR>\n" );
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document.write( "15,000 + 8.50 * x = 45 * x<BR>\n" );
document.write( "subtract 8.50 * x from this both sides of this equation and you get:<BR>\n" );
document.write( "15,000 = 45 * x - 8.50 * x<BR>\n" );
document.write( "simplify to get 15,000 = 36.5 * x.<BR>\n" );
document.write( "divide both sides of this equation by 36.5 to get x = 410.9589041.\r<BR>\n" );
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document.write( "if you sell 410.9589041 items, you will break even.\r<BR>\n" );
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document.write( "45 * 410.9589041 = 18,493.15068 in revenue.\r<BR>\n" );
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document.write( "your cost was 15,000 + 8.5 * 410.9589041 = 18493.15068.\r<BR>\n" );
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document.write( "when you broke even, your profit was 0.\r<BR>\n" );
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document.write( "p(x) = r(x) - c(x) = 0\r<BR>\n" );
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document.write( "p(x) = 36.5 * x - 15,000\r<BR>\n" );
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document.write( "when x = 410.9589041, p(x) becomes 36.5 * 410.9589041 - 15,000 = 0\r<BR>\n" );
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document.write( "do the math and you get 0 = 0 which confirms the equation is true.\r<BR>\n" );
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document.write( "you can also graph these equations.\r<BR>\n" );
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document.write( "the equations to graph are:\r<BR>\n" );
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document.write( "r(x) = 45 * x<BR>\n" );
document.write( "c(x) = 15,000 + 8.5 * x<BR>\n" );
document.write( "p(x) = 36.5 * x - 15,000\r<BR>\n" );
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document.write( "your graph is shown below.\r<BR>\n" );
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document.write( "the red line is the graph of your cost equation.<BR>\n" );
document.write( "the blue line is the graph of your revenue equation.<BR>\n" );
document.write( "the orange line is the graph of your profit equation.\r<BR>\n" );
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document.write( "you break even when your cost is equal to your revenue.\r<BR>\n" );
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document.write( "that happens when the number of items you sell is 410.9589041.\r<BR>\n" );
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document.write( "that's the intersection of your cost line and your revenue line on the graph.\r<BR>\n" );
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document.write( "since you can't sell 410.9958... items, your break even point is between when you sell 410 items and when you sell 411 items.\r<BR>\n" );
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document.write( "your profit when you break even is equal to 0.\r<BR>\n" );
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document.write( "that's shown on the graph of your profit equation.\r<BR>\n" );
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document.write( "profit is equal to revenue - cost.\r<BR>\n" );
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document.write( "at break even, your revenue and your cost are equal so your profit is equal to 0.\r<BR>\n" );
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document.write( "when you sell 600 items, your profit is 6900.\r<BR>\n" );
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document.write( "profit = revenue minus cost.<BR>\n" );
document.write( "when you sell 600 items, your revenue is 27000 and your cost is 20100.<BR>\n" );
document.write( "27000 - 20100 = 6900.\r<BR>\n" );
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document.write( "the graph is showing you what the equations are telling you.\r<BR>\n" );
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