document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173650>Question 1173650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A leading firm requires software for its internal use. The firm wants to evaluate whether it is less<BR>\n" );
document.write( "costly to have its own programming staff and resources or to have programs developed by an<BR>\n" );
document.write( "external development firm. The cost of both options is a function of the number of lines of code.<BR>\n" );
document.write( "After the mathematical analysis, it has been estimated that the in-house development will cost $1.75<BR>\n" );
document.write( "per line of code. In addition, annual overhead costs for supporting the program will be $35000.<BR>\n" );
document.write( "While Software developed outside the firm costs, on average, $2.5 per line of code.\r<BR>\n" );
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document.write( "a) How many lines of code per year make the costs of the two options equal?<BR>\n" );
document.write( "b) If programming needs are estimated at 35000 lines per year, what are the costs of the two<BR>\n" );
document.write( "options?<BR>\n" );
document.write( "c) In part b what would the in-house cost per line of code have to equal for the two options to be<BR>\n" );
document.write( "equally costly?<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 #798919 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=798919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the number of lines of codes.\r<BR>\n" );
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document.write( "inside cost is 35,000 + 1.75 * x<BR>\n" );
document.write( "outside cost is 2.5 * x\r<BR>\n" );
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document.write( "for the costs to be the same, 35,000 + 1.75 * x = 2.5 * x.<BR>\n" );
document.write( "subtract 1.75 * x from both sides of this equation to get:<BR>\n" );
document.write( "35,000 = .75 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 3,5000 / .75 = 46,666.666666...\r<BR>\n" );
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document.write( "the break even point is when x = 46,666.66666....<BR>\n" );
document.write( "that's the number of lines per code per year.\r<BR>\n" );
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document.write( "2.5 * x becomes 2.5 * x = 116,666.66666... lines of code.<BR>\n" );
document.write( "35000 + 1.75 * x = 116,666.66666... lines of code.\r<BR>\n" );
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document.write( "they're the same at the break even point.\r<BR>\n" );
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document.write( "if the programming needs are estimated at 35,000 lines of code per year, then the outside and inside cost would be:\r<BR>\n" );
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document.write( "outside costs = 2.5 * 35,000 = 87,500<BR>\n" );
document.write( "inside costs = 5,000 + 1.75 * 35,000 = 96,250\r<BR>\n" );
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document.write( "to make the costs between inside and outside costs at 35,000 lines of code be the same, then the inside costs would have to be 87,500 as well.\r<BR>\n" );
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document.write( "this could be achieved by reducing the fixed costs or reducing the per line costs are a combination of both.\r<BR>\n" );
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document.write( "assuming the fixed cost have to remain the same, then reduction in the cost per line of code would be the only way.\r<BR>\n" );
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document.write( "let r represent the reduced cost per line of code.<BR>\n" );
document.write( "the equation becomes 87,500 = 35,000 + r * 35,000<BR>\n" );
document.write( "subtract 35,000 from both sides of this equation to get:|<BR>\n" );
document.write( "87,500 - 35,000 = 35,000 * r<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = (87,500 - 35,000) / 35,000 = 52,500 / 35,000 = 1.5 dollars per line of code.\r<BR>\n" );
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document.write( "at that inside cost per line of code, ...\r<BR>\n" );
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document.write( "inside cost = 35,000 + 1.5 * 35,000 = 87,500<BR>\n" );
document.write( "outside cost is 2.5 * 35,000 = 87,500<BR>\n" );
document.write( "they're the same.\r<BR>\n" );
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