document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85175>Question 85175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help....\r<BR>\n" );
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document.write( "Income A baker has 150 units of flour, 90 of sugar, and<BR>\n" );
document.write( "150 of raisins. A loaf of raisin bread requires 1 unit of flour,<BR>\n" );
document.write( "1 of sugar, and 2 of raisins, while a raisin cake needs 5, 2,<BR>\n" );
document.write( "and 1 units, respectively.<BR>\n" );
document.write( "a. If raisin bread sells for $1.75 a loaf and raisin cake for<BR>\n" );
document.write( "$4.00 each, how many of each should be baked so that<BR>\n" );
document.write( "gross income is maximized?<BR>\n" );
document.write( "b. What is the maximum gross income?<BR>\n" );
document.write( "c. Does it require all of the available units of flour, sugar,<BR>\n" );
document.write( "and raisins to produce the number of loaves of raisin<BR>\n" );
document.write( "bread and raisin cakes that produce the maximum profit?<BR>\n" );
document.write( "If not, how much of each ingredient is left over?<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 #61784 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=61784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Income A baker has 150 units of flour, 90 of sugar, and<BR>\n" );
document.write( "150 of raisins. A loaf of raisin bread requires 1 unit of flour,<BR>\n" );
document.write( "1 of sugar, and 2 of raisins, while a raisin cake needs 5, 2,<BR>\n" );
document.write( "and 1 units, respectively.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graphing will be useful here.<BR>\n" );
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document.write( "Let x = no. of loaves of raisin bread<BR>\n" );
document.write( "Let y = no. of raisin cakes<BR>\n" );
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document.write( "Flour equation: <BR>\n" );
document.write( "1x + 5y = 150<BR>\n" );
document.write( "5y = 150 - x<BR>\n" );
document.write( "y = 30 - .2x; green<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Sugar equation<BR>\n" );
document.write( "1x + 2y = 90<BR>\n" );
document.write( "2y = 90 - x<BR>\n" );
document.write( "y = 45 - .5x; purple<BR>\n" );
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document.write( "Raisin equation<BR>\n" );
document.write( "2x + y = 150<BR>\n" );
document.write( "y = 150 - 2x; black<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+140%2C+-10%2C+40%2C+30-.2x%2C45-.5x%2C150-2x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+140%2C+-10%2C+40%2C+30-.2x%2C45-.5x%2C150-2x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "a. If raisin bread sells for $1.75 a loaf and raisin cake for<BR>\n" );
document.write( "$4.00 each, how many of each should be baked so that<BR>\n" );
document.write( "gross income is maximized?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Look at the  corners of the area of feasibility, we have<BR>\n" );
document.write( "x = 0, y = 30<BR>\n" );
document.write( "x = 50, y = 20<BR>\n" );
document.write( "x = 70, y = 10<BR>\n" );
document.write( "x = 75, y = 0<BR>\n" );
document.write( ": <BR>\n" );
document.write( "b. What is the maximum gross income?<BR>\n" );
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document.write( "Using these value for x and y, find the income for each kind.<BR>\n" );
document.write( "x = 50, y = 20 would have the greatest income:<BR>\n" );
document.write( "(1.75*50) + (4 * 20) = $167.50<BR>\n" );
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document.write( "c. Does it require all of the available units of flour, sugar,<BR>\n" );
document.write( "and raisins to produce the number of loaves of raisin<BR>\n" );
document.write( "bread and raisin cakes that produce the maximum profit?<BR>\n" );
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document.write( "No<BR>\n" );
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document.write( "If not, how much of each ingredient is left over?<BR>\n" );
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document.write( "Flour equation:<BR>\n" );
document.write( "1(50) + 5(20) = 150, used all the flour<BR>\n" );
document.write( "Sugar equation:<BR>\n" );
document.write( "1(50) + 2(20) = 90, used all the sugar<BR>\n" );
document.write( "Raisin equation<BR>\n" );
document.write( "2(50) + 1(20) = 140, 150 - 120 = 30 units of raisins left over<BR>\n" );
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document.write( "I think the method is valid, but check my math here.<BR>\n" );
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