document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023712>Question 1023712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, Would you please be able to help me. I need to understand the formula to add into a graphing tool for the following problem:<BR>\n" );
document.write( "A minibus operator is contracted to transport 50 Olympians from the Olympic Village to the Athletic Stadium. He has three type A minibuses and four type B minibuses available. A type A minibus carries 15 people and a type B minibus carries 10 people. Only five drivers are available. It costs $100 to operate a type A minibus and $80 to operate a type B minibus. He wishes to minimise the costs involved to transport the 50 Olympians.<BR>\n" );
document.write( "I've completed the following:<BR>\n" );
document.write( "Variables: Let x represent type A mini bus; Let y represent type B mini bus; Let c represent the minimum cost.<BR>\n" );
document.write( "Constraints:<BR>\n" );
document.write( "x <= 3 (At most 3 type A mini buses available)<BR>\n" );
document.write( "y <= 4 (At most 4 type B mini buses available)<BR>\n" );
document.write( "x + y = 5 (Limit on number of drivers)<BR>\n" );
document.write( "15x + 10y = 50 (Limit on number of passengers who can be carried in both mini buses)<BR>\n" );
document.write( "Objective Function: C = 100x + 80y<BR>\n" );
document.write( "Graphs - I've set the Axis to x: -1 to 10 and y: -1 to 10 and entered the above relations and constraints but don't know how to enter the formula to determine the minimum cost and I don't understand how corner points work.<BR>\n" );
document.write( "Thank you so much for any help you can offer.<BR>\n" );
document.write( "Chris  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #639172 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=639172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A minibus operator is contracted to transport 50 Olympians from the Olympic Village to the Athletic Stadium. He has three type A minibuses and four type B minibuses available. <BR>\n" );
document.write( "A type A minibus carries 15 people and <BR>\n" );
document.write( "A type B minibus carries 10 people.<BR>\n" );
document.write( "------ <BR>\n" );
document.write( "Only five drivers are available.<BR>\n" );
document.write( "---------- <BR>\n" );
document.write( "It costs $100 to operate a type A minibus and $80 to operate a type B minibus.<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "He wishes to minimise the costs involved to transport the 50 Olympians.<BR>\n" );
document.write( "I've completed the following:<BR>\n" );
document.write( "Variables: Let a represent type A mini bus; Let b represent type B mini bus; <BR>\n" );
document.write( "Let c represent the minimum cost.<BR>\n" );
document.write( "Constraints:<BR>\n" );
document.write( "a <= 3 (At most 3 type A mini buses available)<BR>\n" );
document.write( "b <= 4 (At most 4 type B mini buses available)<BR>\n" );
document.write( "a + b <= 5 (Number of drivers)<BR>\n" );
document.write( "15a + 10b <= 50 (Limit on number of passengers who can be carried in both mini buses)<BR>\n" );
document.write( "Objective Function: C = 100a + 80b<BR>\n" );
document.write( "Graphs - I've set the Axis to a: -1 to 3 and b: -1 to 4 and entered the above relations and constraints but don't know how to enter the formula to determine the minimum cost and I don't understand how corner points work.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "f(a)<= -a + 5<BR>\n" );
document.write( "g(a)<= (-3/2)a + 5<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Draw vertical lines at a = 0 and a = 3<BR>\n" );
document.write( "Not <BR>\n" );
document.write( "Draw horizontal lines at b = 0 and b = 4<BR>\n" );
document.write( "Comment:: That describes the solution area.<BR>\n" );
document.write( "Plot f and g in that area.  <BR>\n" );
document.write( "Find their point of interception.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Hope all that helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );