document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103754>Question 103754</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;\"> Baking a try of corn muffins takes 4 c milk and 3 c wheat flour. A tray of bran muffins takes 2 c milk and 3 c wheat flour. A baker has 16 c milk and 15 c wheat flour. He makes $3 profit per tray of corn muffins and $2 profit per tray of bran muffins. How many trays of each type of muffin should the baker make to maximize his profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75436 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=75436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Baking a tray of corn muffins takes 4 c milk and 3 c wheat flour. <BR>\n" );
document.write( "A tray of bran muffins takes 2 c milk and 3 c wheat flour. <BR>\n" );
document.write( "A baker has 16 c milk and 15 c wheat flour.<BR>\n" );
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document.write( "Let corn muffs be \"c\"; bran muffs be \"b\":<BR>\n" );
document.write( "Milk Inequality: 4c + 2b <= 16<BR>\n" );
document.write( "Flour Inequlity: 3c + 3b <= 15<BR>\n" );
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document.write( "Solve each inequality for \"c\":<BR>\n" );
document.write( "Milk: c <- (-1/2)b + 4<BR>\n" );
document.write( "Flour:c <=  -b + 5<BR>\n" );
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document.write( "Graph these inequalities:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B4%2C-x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B4%2C-x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comment: The area enclosed by b=0,c=0,and below the <BR>\n" );
document.write( "intersecting lines is the set of possible values for<BR>\n" );
document.write( "b and c. This is the solution set.<BR>\n" );
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document.write( "He makes $3 profit per tray of corn muffins and $2 profit <BR>\n" );
document.write( "per tray of bran muffins.<BR>\n" );
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document.write( "Object function = 2b + 3c  represents the total profit for<BR>\n" );
document.write( "each combination of b and c in the solution set.<BR>\n" );
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document.write( "Fo find the maximum profit test the vertices of the solution set in the<BR>\n" );
document.write( "object function:<BR>\n" );
document.write( "The vertices are:<BR>\n" );
document.write( "(0,0) which gives 2*0+3*0 = 0  profit<BR>\n" );
document.write( "(0,4) which gives profit = 2*0+3*4 = 12 <BR>\n" );
document.write( "(2,3) which gives profit = 2*2+3*3 = 13<BR>\n" );
document.write( "(5,0) which gives profit = 2*5+3*0 = 10<BR>\n" );
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document.write( "How many trays of each type of muffin should the baker make to maximize his profit?<BR>\n" );
document.write( "two trays of bran and three trays of corn<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );