document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141850>Question 1141850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A product may be made using Machine I or Machine II. The manufacturer estimates that the monthly fixed costs of using Machine I are $19,000, whereas the monthly fixed costs of using Machine II are $15,000. The variable costs of manufacturing 1 unit of the product using Machine I and Machine II are $13 and $19, respectively. The product sells for $60 each. <BR>\n" );
document.write( "(a) Find the cost functions C(x) associated with using each machine, where x is the number of units produced using that machine. <BR>\n" );
document.write( "Machine I    	C1(x)	 = 	<BR>\n" );
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document.write( "Machine II    	C2(x)	 = 	<BR>\n" );
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document.write( "(b) Sketch the graphs of the cost functions of part (a) and the revenue function on the same set of axes. (Sketch the graphs using rays.)\r<BR>\n" );
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document.write( "(c) Which machine should management choose to maximize their profit if the projected sales are 450 units? <BR>\n" );
document.write( "Machine I<BR>\n" );
document.write( "Machine II    \r<BR>\n" );
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document.write( "Which machine should management choose to maximize their profit if the projected sales are 550 units?<BR>\n" );
document.write( "Machine I<BR>\n" );
document.write( "Machine II    \r<BR>\n" );
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document.write( "Which machine should management choose to maximize their profit if the projected sales are 650 units?<BR>\n" );
document.write( "Machine I<BR>\n" );
document.write( "Machine II    \r<BR>\n" );
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document.write( "(d) What is the profit for each case in part (c)? <BR>\n" );
document.write( "450 units    	$  <BR>\n" );
document.write( "550 units    	$  <BR>\n" );
document.write( "650 units    	$  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762487 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=762487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cost function for machine 1 is 19000 + 13 * x.\r<BR>\n" );
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document.write( "cost function for machine 2 is 15000 + 19 * x.\r<BR>\n" );
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document.write( "revenue function is 60 * x\r<BR>\n" );
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document.write( "x represents the number of units produced and sold.\r<BR>\n" );
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document.write( "when 450 units are sold ........,\r<BR>\n" );
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document.write( "revenue is 60 * 450 = 27,000<BR>\n" );
document.write( "cost using machine 1 is 19000 + 13 * 450 = 24,850<BR>\n" );
document.write( "cost using machine 2 is 15000 + 19 * 450 = 23,550\r<BR>\n" );
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document.write( "profit using machine 1 is 27,000 - 24,850 = 2,150<BR>\n" );
document.write( "profit using machine 2 is 27,000 - 23,550 = 3,450\r<BR>\n" );
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document.write( "profit using machine 2 is more than profit using machine 1.\r<BR>\n" );
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document.write( "when 550 units are sold .........,\r<BR>\n" );
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document.write( "revenue is 60 * 550 = 33,000<BR>\n" );
document.write( "cost using machine 1 is 19000 + 13 * 550 = 26,150<BR>\n" );
document.write( "cost using machine 2 is 15000 + 19 * 550 = 25,450\r<BR>\n" );
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document.write( "profit using machine 1 is 33,000 - 26,150 = 6,850<BR>\n" );
document.write( "profit using machine 2 is 33,000 - 25,450 = 7,550\r<BR>\n" );
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document.write( "profit using machine 2 is more than profit using machine 1.\r<BR>\n" );
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document.write( "when 650 units are sold .............,\r<BR>\n" );
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document.write( "revenue is 60 * 650 = 39,000<BR>\n" );
document.write( "cost using machine 1 is 19000 + 13 * 650 = 27,450<BR>\n" );
document.write( "cost using machine 2 is 15000 + 19 * 650 = 27,350 \r<BR>\n" );
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document.write( "profit using machine 1 is 39,000 - 27,450 = 11,550<BR>\n" );
document.write( "profit using machine 2 is 39,000 - 27,350 = 11,650\r<BR>\n" );
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document.write( "profit using machine 2 is more than profit using machine 1.\r<BR>\n" );
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document.write( "profit is equal to revenue minus cost.<BR>\n" );
document.write( "if the revenue is the same regardless of which machine is used, then the greater profit is given to the machine that uses the least cost.\r<BR>\n" );
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document.write( "the break even point where the cost for using machine 1 versus using machine 2 is found by making their cost functions equal to each other.\r<BR>\n" );
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document.write( "you get 19000 + 13 * x = 15000 + 19 * x<BR>\n" );
document.write( "subtract 15000 from both sides of this equation and subtract 13 * x from both sides of this equation to get 19000 - 15000 = 19 * x - 13 * x.<BR>\n" );
document.write( "combine like terms to get 4000 = 6 * x<BR>\n" );
document.write( "solve for x to get x = 666.67 units.<BR>\n" );
document.write( "with that number of units, the cost of using machine 1 is the same as the cost of using machine 2.<BR>\n" );
document.write( "when the number of units produced and sold are greater than that, machine 1 provides more profit.\r<BR>\n" );
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document.write( "for example, when 750 units are produced .........,<BR>\n" );
document.write( "revenue is 60 * 750 = 45,000<BR>\n" );
document.write( "cost for machine 1 is 19000 + 13 * 750 = 28,750<BR>\n" );
document.write( "cost for machine 2 is 15000 + 19 * 750 = 29,250<BR>\n" );
document.write( "profit for machine 1 is 45,000 - 28,750 = 16,250<BR>\n" );
document.write( "profit for machine 2 is 45,000 - 29,250 = 15,750\r<BR>\n" );
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document.write( "profit using machine 1 is more than profit using machine 2.\r<BR>\n" );
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document.write( "the following graph shows revenue and cost at 450, 550, 650, and 750 units.\r<BR>\n" );
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document.write( "graph of revenue is green.<BR>\n" );
document.write( "graph of cost for machine 1 is red.<BR>\n" );
document.write( "graph of cost for machine 2 is blue\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/060401.jpg\" alt=\"$$$\" >\r<BR>\n" );
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