document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121751>Question 121751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i. Use trial and error to find the quantity of tile sets per month that yields the highest profit.<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 #89395 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1 i\r<BR>\n" );
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document.write( "Notice that in part g) we had a profit of $475 (which was the largest profit so far). So let's increase x until we find the highest profit.\r<BR>\n" );
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document.write( "Let's find the profit when 26 tiles are sold:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-1x%5E2%2B56x-300 ALIGN=MIDDLE  ALT=\"f%28x%29=-1x%5E2%2B56x-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2826%29=-1%2826%29%5E2%2B56%2826%29-300 ALIGN=MIDDLE  ALT=\"f%2826%29=-1%2826%29%5E2%2B56%2826%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=26 ALIGN=MIDDLE  ALT=\"x=26\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with 26.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2826%29=-1%28676%29%2B56%2826%29-300 ALIGN=MIDDLE  ALT=\"f%2826%29=-1%28676%29%2B56%2826%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%29%5E2 ALIGN=MIDDLE  ALT=\"%2826%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 676.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2826%29=-676%2B56%2826%29-300 ALIGN=MIDDLE  ALT=\"f%2826%29=-676%2B56%2826%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -1 and 676 to get  -676\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2826%29=-676%2B1456-300 ALIGN=MIDDLE  ALT=\"f%2826%29=-676%2B1456-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 56 and 26 to get  1456\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2826%29=480 ALIGN=MIDDLE  ALT=\"f%2826%29=480\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the when 26 tiles are sold, the profit is $480\r<BR>\n" );
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document.write( "Let's find the profit when 27 tiles are sold:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-1x%5E2%2B56x-300 ALIGN=MIDDLE  ALT=\"f%28x%29=-1x%5E2%2B56x-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2827%29=-1%2827%29%5E2%2B56%2827%29-300 ALIGN=MIDDLE  ALT=\"f%2827%29=-1%2827%29%5E2%2B56%2827%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=27 ALIGN=MIDDLE  ALT=\"x=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with 27.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2827%29=-1%28729%29%2B56%2827%29-300 ALIGN=MIDDLE  ALT=\"f%2827%29=-1%28729%29%2B56%2827%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2827%29%5E2 ALIGN=MIDDLE  ALT=\"%2827%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 729.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2827%29=-729%2B56%2827%29-300 ALIGN=MIDDLE  ALT=\"f%2827%29=-729%2B56%2827%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -1 and 729 to get  -729\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2827%29=-729%2B1512-300 ALIGN=MIDDLE  ALT=\"f%2827%29=-729%2B1512-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 56 and 27 to get  1512\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2827%29=483 ALIGN=MIDDLE  ALT=\"f%2827%29=483\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the when 27 tiles are sold, the profit is $483\r<BR>\n" );
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document.write( "Let's find the profit when 28 tiles are sold:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-1x%5E2%2B56x-300 ALIGN=MIDDLE  ALT=\"f%28x%29=-1x%5E2%2B56x-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2828%29=-1%2828%29%5E2%2B56%2828%29-300 ALIGN=MIDDLE  ALT=\"f%2828%29=-1%2828%29%5E2%2B56%2828%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=28 ALIGN=MIDDLE  ALT=\"x=28\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with 28.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2828%29=-1%28784%29%2B56%2828%29-300 ALIGN=MIDDLE  ALT=\"f%2828%29=-1%28784%29%2B56%2828%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2828%29%5E2 ALIGN=MIDDLE  ALT=\"%2828%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 784.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2828%29=-784%2B56%2828%29-300 ALIGN=MIDDLE  ALT=\"f%2828%29=-784%2B56%2828%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -1 and 784 to get  -784\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2828%29=-784%2B1568-300 ALIGN=MIDDLE  ALT=\"f%2828%29=-784%2B1568-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 56 and 28 to get  1568\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2828%29=484 ALIGN=MIDDLE  ALT=\"f%2828%29=484\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the when 28 tiles are sold, the profit is $484\r<BR>\n" );
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document.write( "Let's find the profit when 29 tiles are sold:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-1x%5E2%2B56x-300 ALIGN=MIDDLE  ALT=\"f%28x%29=-1x%5E2%2B56x-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2829%29=-1%2829%29%5E2%2B56%2829%29-300 ALIGN=MIDDLE  ALT=\"f%2829%29=-1%2829%29%5E2%2B56%2829%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=29 ALIGN=MIDDLE  ALT=\"x=29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with 29.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2829%29=-1%28841%29%2B56%2829%29-300 ALIGN=MIDDLE  ALT=\"f%2829%29=-1%28841%29%2B56%2829%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829%29%5E2 ALIGN=MIDDLE  ALT=\"%2829%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 841.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2829%29=-841%2B56%2829%29-300 ALIGN=MIDDLE  ALT=\"f%2829%29=-841%2B56%2829%29-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -1 and 841 to get  -841\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2829%29=-841%2B1624-300 ALIGN=MIDDLE  ALT=\"f%2829%29=-841%2B1624-300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 56 and 29 to get  1624\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2829%29=483 ALIGN=MIDDLE  ALT=\"f%2829%29=483\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the when 29 tiles are sold, the profit is $483\r<BR>\n" );
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document.write( "Notice how the profit is steadily increasing from x=26 to x=28. However, it starts to decrease after x=28. So this shows that the highest profit of $484 occurs when 28 tiles are sold.<BR>\n" );
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