document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174531>Question 174531</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131339982/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> While stranded on an island, the crew of a sailboat has access to only three sources of food, as shown in the table below. One of the crew members designs a daily diet to supply each person with 120g of fat, 220g of carbohydrates, and 80g of protein.\r<BR>\n" );
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document.write( "_______________  A______B_______C<BR>\n" );
document.write( "Fat____________	10 g____ 4g_____ 12 g<BR>\n" );
document.write( "Carbohydrates___11 g___77 g_____0g<BR>\n" );
document.write( "Protein_________4 g_____1 g_____16 g\r<BR>\n" );
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document.write( "A. Write a system of three equations in three variables to find the number of portions of each food each person must have to meet the daily diet.<BR>\n" );
document.write( "B. Use an augmented matrix to solve the system of equations from part (a).<BR>\n" );
document.write( "C. Suppose food C runs out. How would this change the number of portions of food required each day?<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 #129598 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=129598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 120g of fat, 220g of carbohydrates, and 80g of protein. <BR>\n" );
document.write( "_______________ A______B_______C<BR>\n" );
document.write( "Fat____________ 10 g____ 4g_____ 12 g<BR>\n" );
document.write( "Carbohydrates___11 g___77 g_____0g<BR>\n" );
document.write( "Protein_________4 g_____1 g_____16 g <BR>\n" );
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document.write( "A)10A+4B+12C=120<BR>\n" );
document.write( "  11A+77B   =220<BR>\n" );
document.write( "   4A+ 1B+16C=80<BR>\n" );
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document.write( "B)using cramers rule<BR>\n" );
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document.write( "find determinant of main matrix<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C10%2C4%2C12%2C11%2C77%2C0%2C4%2C1%2C16%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C10%2C4%2C12%2C11%2C77%2C0%2C4%2C1%2C16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >using column 3---> 12<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C11%2C77%2C4%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C11%2C77%2C4%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-0<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C10%2C4%2C4%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C10%2C4%2C4%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+16<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C10%2C4%2C11%2C77%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C10%2C4%2C11%2C77%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---->12(-297)+16(726)=8052<BR>\n" );
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document.write( "A=det<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C120%2C4%2C12%2C220%2C77%2C0%2C80%2C1%2C16%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C120%2C4%2C12%2C220%2C77%2C0%2C80%2C1%2C16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/8052---->so using the 3rd column--->det = 12<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C220%2C77%2C80%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C220%2C77%2C80%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-0+16<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C120%2C4%2C220%2C77%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C120%2C4%2C220%2C77%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--->12(-5940)+16(8360)=62480<BR>\n" );
document.write( ":<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=62480%2F8052=7.76%29 ALIGN=MIDDLE  ALT=\"highlight%28A=62480%2F8052=7.76%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "B=det<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C10%2C120%2C12%2C11%2C220%2C0%2C4%2C80%2C16%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C10%2C120%2C12%2C11%2C220%2C0%2C4%2C80%2C16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/8052---->so using the 3rd column--->det = 12<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C11%2C220%2C4%2C80%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C11%2C220%2C4%2C80%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-0+16<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C10%2C120%2C11%2C220%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C10%2C120%2C11%2C220%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---->0+16(880)=14080<BR>\n" );
document.write( ":<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=14080%2F8052=1.75%29 ALIGN=MIDDLE  ALT=\"highlight%28B=14080%2F8052=1.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "C=det<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C10%2C4%2C120%2C11%2C77%2C220%2C4%2C1%2C80%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C10%2C4%2C120%2C11%2C77%2C220%2C4%2C1%2C80%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/8052---->using column 1--->det= 10<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C77%2C220%2C1%2C80%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C77%2C220%2C1%2C80%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-11<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C4%2C120%2C1%2C80%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C4%2C120%2C1%2C80%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C4%2C120%2C77%2C220%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C4%2C120%2C77%2C220%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--->10(5940)-11(200)+4(-8360)--->59400-2200-33440=<BR>\n" );
document.write( "23760<BR>\n" );
document.write( ":<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=23760%2F8052=4.37%29 ALIGN=MIDDLE  ALT=\"highlight%28C=23760%2F8052=4.37%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "C)if C was no longer available we would have the equation<BR>\n" );
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document.write( "10A+4B+0C=120<BR>\n" );
document.write( "11A+77B+0C=220<BR>\n" );
document.write( " 4A+  B+0C=80<BR>\n" );
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document.write( "we cannot use Cramers rule because there would be no unique solution as the determinant you would be dividing by would be zero.<BR>\n" );
document.write( ":according to this graph there is no unique solution to this scenario.<BR>\n" );
document.write( "It appears you could reach 2 of the conditions in any order but not all 3 at once.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-100%2C50%2C-100%2C50%2C%28-5%2F2%29x%2B30%2C%28-1%2F7%29x%2B220%2F77%2C-4x%2B80%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );