document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209077>Question 209077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the minumum value of f(x,y)=2x-y+2 for the polygonal convex set determined by this system of inequalities:x>=1, x<=3, y>=0, 1/2x + y<=5.\r<BR>\n" );
document.write( "\n" );
document.write( "A)0\r<BR>\n" );
document.write( "\n" );
document.write( "B)-3\r<BR>\n" );
document.write( "\n" );
document.write( "C)3\r<BR>\n" );
document.write( "\n" );
document.write( "D)-0.5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158173 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=158173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To  best  visualize  this  problem,  please  draw  on  a  standard  x-y  coordinate  system,  the  area  of  concern.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(1) x>=1,,,,   to  the  right  of  a  vertical  line  at  x=1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(2) x<=3,,,,,to  the  left  of  a  vertical  line  at  x=3<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(3) y>=0,,,,,,,above  a  horizontal  line  at  y=0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(4) (x/2) +y <= 5,,,,,below  a  line  from (1,4.5)  to (3,3.5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now,  to  find  the  min of  f(x,y) = 2x -y +2,,,let's  look  at  the  corners  of  the  area  of  concern,,,by  just  substituting coordinate  values  in function<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(1,0),,,,,f(x,y) = 4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(1, 4.5),,,f(x,y) = -.5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(3,3.5),,,,f(x,y) = .5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(3,0),,,,,f(x,y) = 8<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "It  appears  to  be  a  min  at  -.5, which  is  answer (D)<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );