document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160662>Question 1160662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Helen and David are playing a game by putting chips in two piles (each player has two<BR>\n" );
document.write( "piles P1 and P2), respectively. Helen has 6 chips and David has 4 chips. Each player<BR>\n" );
document.write( "places his/her chips in his/her two piles, then compare the number of chips in his/her<BR>\n" );
document.write( "two piles with that of the other player’s two piles. Note that once a chip is placed in one<BR>\n" );
document.write( "pile it cannot be moved to another pile. There are four comparisons including Helen’s<BR>\n" );
document.write( "P1 vs David’s P1, Helen’s P1 vs David’s P2, Helen’s P2 vs David’s P1, and Helen’s P2<BR>\n" );
document.write( "vs David’s P2. For each comparison, the player with more chips in the pile will score 1<BR>\n" );
document.write( "point (the opponent will lose 1 point). If the number of chips is the same in the two piles,<BR>\n" );
document.write( "then nobody will score any points from this comparison. The final score of the game is<BR>\n" );
document.write( "the sum score over the four comparisons. For example, if Helen puts 5 and 1 chips in her<BR>\n" );
document.write( "P1 and P2, David puts 3 and 1 chips in his P1 and P2, respectively. Then Helen will get<BR>\n" );
document.write( "1 (5 vs 3) + 1 (5 vs 1) - 1 (1 vs 3) + 0 (1 vs 1) = 1 as her final score, and David will get<BR>\n" );
document.write( "his final score of -1.<BR>\n" );
document.write( "(a) Give reasons why/how this game can be described as a two-players-zero-sum game.<BR>\n" );
document.write( "(b) Formulate the payoff matrix for the game.<BR>\n" );
document.write( "(c) Explain what is a saddle point. Verify: does the game have a saddle point?<BR>\n" );
document.write( "(d) Construct a linear programming model for each player in this game;<BR>\n" );
document.write( "(e) Produce an appropriate code to solve the linear programming model in part (c).<BR>\n" );
document.write( "(f) Solve the game for David using the linear programming model you constructed in<BR>\n" );
document.write( "part (d). Interpret your solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784079 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=784079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Looks like an entire semester of problem(s).<BR>\n" );
document.write( "Good luck with that.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );