document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972155>Question 972155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Classify the following problems as to whether they are pure-integer, mixed-integer, zero-one, goal, or nonlinear programming problems.\r<BR>\n" );
document.write( "\n" );
document.write( "Maximize Z = 5 X1 + 6 X1 X2 + 2 X2<BR>\n" );
document.write( "Subject to: 3 X1 + 2 X2 &#8805; 6<BR>\n" );
document.write( "X1 + X2 &#8804; 8<BR>\n" );
document.write( "X1, X2 &#8805; 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Minimize Z = 8 X1 + 6 X2<BR>\n" );
document.write( "Subject to: 4 X1 + 5 X2 &#8805; 10<BR>\n" );
document.write( "X1 + X2 &#8804; 3<BR>\n" );
document.write( "X1, X2 &#8805; 0<BR>\n" );
document.write( "X1, X2 = 0 or 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Maximize Z = 10 X1 + 5 X2<BR>\n" );
document.write( "Subject to: 8 X1 + 10 X2 = 10<BR>\n" );
document.write( "4 X1 + 6 X2 &#8805; 5<BR>\n" );
document.write( "X1, X2 integer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Minimize Z = 8 X12 + 4 X1 X2 + 12 X22<BR>\n" );
document.write( "Subject to: 6 X1 + X2 &#8805; 50<BR>\n" );
document.write( "X1 + X2 &#8805; 40\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594529 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first one and the last one are non-linear because the objective functions have an <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x_1x_2\"> term.  Since linear functions have terms that are all of degree 1 and an <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x_1x_2\"> is of degree 2 (you sum the exponents in a term to find the degree, in this case 1 + 1 = 2), the function is non-linear.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The second one is zero-one because the variables are constrained to zero or one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The third one is pure integer because both variables are constrained to the  integers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );