document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118030>Question 1118030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manager is trying to decide whether to purchase a certain part or to have it produced internally.Internal production could use either of two processes. One would entail a variable cost of $17 perunit and an annual fixed cost of $200,000; the other would entail a variable cost of $14 per unitand an annual fixed cost of $240,000. Three vendors are willing to provide the part. Vendor A hasa price of $20 per unit for any volume up to 30,000 units. Vendor B has a price of $22 per unit fordemand of 1,000 units or less, and $18 per unit for larger quantities. Vendor C offers a price of $21per unit for the first 1,000 units, and $19 per unit for additional units.<BR>\n" );
document.write( "a.	If the manager anticipates an annual volume of 10,000 units, which alternative would be bestfrom a cost standpoint? For 20,000 units, which alternative would be best?<BR>\n" );
document.write( "b.	Determine the range for which each alternative is best. Are there any alternatives that are never best? Which?<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 #733245 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=733245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> from 1 to 1000, vendor A is the cheapest.\r<BR>\n" );
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document.write( "this is because vendor A unit cost is 20 dollars while vendor B unit cost is 22 dollars and vendor C unit cost is 21 dollars.\r<BR>\n" );
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document.write( "internal option 1 and 2 are not considered because their minimum cost is 200,000 and 240,000 dollars respectively.\r<BR>\n" );
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document.write( "at 1000 units, vendor A, who is the cheapest of the vendors, has a total cost of 1000 * 20 = 20,000 dollars, which is well below the threshold of either of the internal options.\r<BR>\n" );
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document.write( "between 1001 and 59,999 units, vendor B is the cheapest.\r<BR>\n" );
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document.write( "this is because vendor B unit cost is 18 dollars while vendor A unit cost is still 20 dollars and vendor C unit cost is 19 dollars.\r<BR>\n" );
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document.write( "this continues until 60,000 units, at which time vendor B total cost and internal option 2 total cost are the same.\r<BR>\n" );
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document.write( "vendor B total cost is 60,000 * 18 = 1,080,000 dollars.<BR>\n" );
document.write( "internal option 2 total cost is 240,000 + 14 * 60,000 = 1,080,000 dollars.\r<BR>\n" );
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document.write( "after 60,000 units, internal option 2 becomes, and stays, the cheapest.\r<BR>\n" );
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document.write( "Vendor C and internal option 1 are never the cheapest.\r<BR>\n" );
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document.write( "the break even point for the two internal options is determined as follows:\r<BR>\n" );
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document.write( "200,000 + 17x = 240,000 + 14x<BR>\n" );
document.write( "subtract 14x from both sides and subtract 200,000 from both sides to get:<BR>\n" );
document.write( "17x - 14x = 240,000 - 200,000<BR>\n" );
document.write( "simplify to get 3x = 40,000<BR>\n" );
document.write( "solve for x to get x - 13,333.33333333.....\r<BR>\n" );
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document.write( "13,334 units is when internal option 2 becomes cheaper than internal option 1.\r<BR>\n" );
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document.write( "at 13,334 units:\r<BR>\n" );
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document.write( "internal option 1 = 200,000 + 13,334 * 17 = 426,678<BR>\n" );
document.write( "internal option 2 = 240,000 + 13,334 * 14 = 426,676\r<BR>\n" );
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document.write( "after 13,334 units, internal option 2 is the cheapest of the two.\r<BR>\n" );
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document.write( "at 13,334, the cheapest of the vendors, which is vendor B, total cost is 13,334 * 18 = 240,012.\r<BR>\n" );
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document.write( "vendor B continues to be the cheapest until 60,000 units, at which time vendor B and internal option 2 are tied at 1,080,000 dollars each.\r<BR>\n" );
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document.write( "after 60,000 units, internal option 2 takes over forever.\r<BR>\n" );
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document.write( "so, there you have it.\r<BR>\n" );
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document.write( "Vendor A cheapest to 1000 units.<BR>\n" );
document.write( "vendor B cheapest from 1001 to 59,999 units.<BR>\n" );
document.write( "vendor B and internal option 2 ties at 60,000 units.<BR>\n" );
document.write( "internal option 2 cheapest from 60,001 units up.<BR>\n" );
document.write( "vendor C and internal option 1 never the cheapest.\r<BR>\n" );
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document.write( "note that vendor A never gave an estimate for greater than 30,000 units.<BR>\n" );
document.write( "in absence of any additional information on vendor A, i kept him at 20 dollars a unit.<BR>\n" );
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