document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209247>Question 209247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)Two varieties of animal feed contain essential nutrients A and B.  Feed I contains 2 units of A and 3 units of B per pound.  Feed II contains 2 units of A and 5 units of B per pound.  A farmer needs a feed mix that will give his animals a minimum of 16 units of A and 30 units of B.  If Feed I costs $3 per pound and Feed II costs $4 per pound, how much of each should be bought to supply the proper nutrition while minimizing cost?  Write the objective function and system of linear inequalities and solve it graphically using the method of corners.<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 #158177 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=158177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two varieties of animal feed contain essential nutrients A and B. <BR>\n" );
document.write( "Feed I contains 2 units of A and 3 units of B per pound. <BR>\n" );
document.write( "Feed II contains 2 units of A and 5 units of B per pound. <BR>\n" );
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document.write( "A farmer needs a feed mix that will give his animals a minimum of 16 units of A and 30 units of B.<BR>\n" );
document.write( "\"A\" Eq.: 2(I)+2(II) >= 16<BR>\n" );
document.write( "\"B\" Eq.: 3(I)+5(II) >= 30<BR>\n" );
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document.write( "If Feed I costs $3 per pound and Feed II costs $4 per pound, how much of each should be bought to supply the proper nutrition while minimizing cost?<BR>\n" );
document.write( "Cost Eq: C(x) = 3(I) + 4(II) <BR>\n" );
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document.write( "Write the objective function and system of linear inequalities and solve it graphically using the method of corners.<BR>\n" );
document.write( "I >=0<BR>\n" );
document.write( "II >=0<BR>\n" );
document.write( "\"A\"Eq: I >= -II+8<BR>\n" );
document.write( "\"B\"Eq: I >= (-5/3)(II) + 10<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C30%2C-10%2C30%2C-x%2B8%2C%28-5%2F3%29x%2B10%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C30%2C-10%2C30%2C-x%2B8%2C%28-5%2F3%29x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(II,I) Corners:  (0,8), (6,0), (3,5)<BR>\n" );
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document.write( "Objective:<BR>\n" );
document.write( "C(x) = 3(I) + 4(II)<BR>\n" );
document.write( "(0,8) C(x) = 3*8+4*0 = 24<BR>\n" );
document.write( "(6,0) C(x) = 3*0+4*6 = 24<BR>\n" );
document.write( "(3,5) C(x) = 3*5+4*3 = 27<BR>\n" );
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document.write( "Minimal Cost : 8 of I or 6 of II<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "Reply to stanbon@comcast.net </SPAN>\n" );
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