document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=720485>Question 720485</A>: <I><SPAN STYLE=\"word-break: break-all;\">  \r<BR>\n" );
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document.write( "5.&#8203;A company that builds phones earns a profit on sales according to the quadratic relation\r<BR>\n" );
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document.write( "                 P =          -10n2 + 1000n -2500\r<BR>\n" );
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document.write( "where P is the profit earned in dollars, and N is the number of crates of phones sold.\r<BR>\n" );
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document.write( "a.       How many crates must be sold to make a maximum profit?\r<BR>\n" );
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document.write( "b.      What is the maximum profit that can be made?\r<BR>\n" );
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document.write( "c.       If you sell 11 crates how will you make a profit or a loss?  How much?\r<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 #441849 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=441849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5.&#8203;A company that builds phones earns a profit on sales according to the quadratic relation<BR>\n" );
document.write( "P = -10n2 + 1000n -2500<BR>\n" );
document.write( "where P is the profit earned in dollars, and N is the number of crates of phones sold.\r<BR>\n" );
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document.write( "a. How many crates must be sold to make a maximum profit?<BR>\n" );
document.write( "P = -10n^2 + 1000n -2500<BR>\n" );
document.write( "Find derivative:<BR>\n" );
document.write( "P' = -20n + 1000<BR>\n" );
document.write( "Set P' to zero to find critical points:<BR>\n" );
document.write( "0 = -20n + 1000<BR>\n" );
document.write( "-1000 = -20n<BR>\n" );
document.write( "1000 = 20n<BR>\n" );
document.write( "100 = 2n<BR>\n" );
document.write( "50 = n<BR>\n" );
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document.write( "b. What is the maximum profit that can be made?<BR>\n" );
document.write( "plug n=50 and find P:<BR>\n" );
document.write( "P = -10n^2 + 1000n -2500<BR>\n" );
document.write( "P = -10(50)^2 + 1000(50) -2500<BR>\n" );
document.write( "P = -10(2500) + 1000(50) -2500<BR>\n" );
document.write( "P = -25000 + 50000 -2500<BR>\n" );
document.write( "P = 25000 -2500<BR>\n" );
document.write( "P = $22500<BR>\n" );
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document.write( "c. If you sell 11 crates how will you make a profit or a loss? How much?<BR>\n" );
document.write( "plug n=11 and find P:<BR>\n" );
document.write( "P = -10n^2 + 1000n -2500<BR>\n" );
document.write( "P = -10(11)^2 + 1000(11) -2500<BR>\n" );
document.write( "P = -10(121) + 11000 -2500<BR>\n" );
document.write( "P = -1210 + 11000 -2500<BR>\n" );
document.write( "P = 9790 -2500<BR>\n" );
document.write( "P = $7290 (Profit)<BR>\n" );
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