document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21915>Question 21915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An orange grower has 400 crates of fruit ready to ship and will have 20 more for each day he waits.  The current price is $60 per crate and will drop an estimated $2 per day for each day he waits.  In how many days should he ship to maximize his income and what is his maximum income?\r<BR>\n" );
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document.write( "I tried to set up a equation like this:  (400+20d)(60-2d)=i, but since it drops an estimated $2 a day, I'm don't think this is the right formula. Can you help?  THANKS! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10612 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the profit is proportional to total income. we don't know the growers other<BR>\n" );
document.write( "expenses he has to pay out. <BR>\n" );
document.write( "my equation for total income is:<BR>\n" );
document.write( "I = income<BR>\n" );
document.write( "c = crates<BR>\n" );
document.write( "#d = days passed<BR>\n" );
document.write( "I = (400 c x $60 / c) + (20 c /d x #d)($60/c - ($2/d)/c x #d)<BR>\n" );
document.write( "I = 400 x 60 + (20d)(60 - 2d)<BR>\n" );
document.write( "I = 24000 + 1200d -40d^2<BR>\n" );
document.write( "I = 2400 + 120 d - 4d^2<BR>\n" );
document.write( "I = 600 + 30d - d^2<BR>\n" );
document.write( "for a max or min I want I' the dirivative to be zero<BR>\n" );
document.write( "0 = 30 - 2d<BR>\n" );
document.write( "2d = 30<BR>\n" );
document.write( "d = 15<BR>\n" );
document.write( "I'll test for 14, 15 and 16 days to see if 15 days really is a maximum\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I+=+400+%2A+60+%2B+%2820+%2A+14%29%2860+-+%282+%2A+14%29%29 ALIGN=MIDDLE  ALT=\"I+=+400+%2A+60+%2B+%2820+%2A+14%29%2860+-+%282+%2A+14%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I = 24,000 + 8,960<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I+=+400+%2A+60+%2B+%2820+%2A+16%29%2860+-+%282+%2A+16%29%29 ALIGN=MIDDLE  ALT=\"I+=+400+%2A+60+%2B+%2820+%2A+16%29%2860+-+%282+%2A+16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "I = 24,000 + 8,960<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I+=+400+%2A+60+%2B+%2820+%2A+15%29%2860+-+%282+%2A+15%29%29 ALIGN=MIDDLE  ALT=\"I+=+400+%2A+60+%2B+%2820+%2A+15%29%2860+-+%282+%2A+15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I = 24,000 + 9,000<BR>\n" );
document.write( "15 is a maximum<BR>\n" );
document.write( "if you have not had calculus, you can use trial and error to get same result </SPAN>\n" );
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