document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73077>Question 73077</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0030522234/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A tourist agency can sell up to 1200 travel packages for a football game. The package includes airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight. The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers. The agency can locate no more than 10 planes for the travel packages. Each package with nonstop flight sells for $1200, and each package with a two-stop flight sells for $900. Assume that each plane will carry the maximum number of passengers.What is the system of inequlities? Can you show me the feasbile region on a graph? What is the objective function minimized or maximized? What is the coordinate of the vertices of the feasible region?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52359 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=52359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A tourist agency can sell up to 1200 travel packages for a football game. The package includes airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight. The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers. The agency can locate no more than 10 planes for the travel packages. Each package with nonstop flight sells for $1200, and each package with a two-stop flight sells for $900. Assume that each plane will carry the maximum number of passengers.What is the system of inequalities? Can you show me the feasibility region on a graph? What is the objective function minimized or maximized? What is the coordinate of the vertices of the feasible region?<BR>\n" );
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document.write( "Let x = number of 150 passenger planes (1 stop)<BR>\n" );
document.write( "Let y = number of 100 passenger planes (2 stop)<BR>\n" );
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document.write( "Number of airplanes:<BR>\n" );
document.write( "x + y =< 10<BR>\n" );
document.write( "Put in the general (y=) form, to plot on a graph<BR>\n" );
document.write( "y =< 10 - x; (purple line)<BR>\n" );
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document.write( "Number of travel packages sold:<BR>\n" );
document.write( "150x + 100y =< 1200<BR>\n" );
document.write( "100y =< 1200 - 150x<BR>\n" );
document.write( "y =< 1200/100 - (150/100)x<BR>\n" );
document.write( "y =< 12 - 1.5x; (green line)<BR>\n" );
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document.write( "The graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+12%2C+-2%2C+15%2C+10-x%2C+12-1.5x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+12%2C+-2%2C+15%2C+10-x%2C+12-1.5x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Feasibility region is at or below the purple or green lines whichever is lowest<BR>\n" );
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document.write( "The vertices:<BR>\n" );
document.write( "1.x = 8, y = 0: 8*150*1200 = $1,440,000 revenue; 8 ea 150 pass planes only<BR>\n" );
document.write( "2.x = 0, y = 10: 10*100*900 = $900,000 revenue; 10 ea 100 pass planes only<BR>\n" );
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document.write( "Solve the two equation system to find the 3rd vertici<BR>\n" );
document.write( "150x + 100y = 1200<BR>\n" );
document.write( "Simplify, divide by 100<BR>\n" );
document.write( "1.5x + y = 12 <BR>\n" );
document.write( "x + y = 10<BR>\n" );
document.write( "----------------subtract, find x<BR>\n" );
document.write( ".5x = 2<BR>\n" );
document.write( "x = 2/.5<BR>\n" );
document.write( "x = 4<BR>\n" );
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document.write( "Find y:<BR>\n" );
document.write( "4 + y = 10<BR>\n" );
document.write( "y = 6<BR>\n" );
document.write( "The 3rd vertici is x = 4, y = 6, 4 ea 150 pass planes, 6 ea 100 pass planes<BR>\n" );
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document.write( "Revenue:<BR>\n" );
document.write( "4*150*1200 = $720,000<BR>\n" );
document.write( "6*100*900  = $540,000<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "The total= $1,260,000 for 4 ea 150 pass planes and 6 ea 100 pass planes<BR>\n" );
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document.write( "Max revenue would be 8 full 150 pass planes at $1,440,000<BR>\n" );
document.write( "Min revenue would be 10 full 100 pass planes at $900,000<BR>\n" );
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