View of /trunk/NationalProblemLibrary/ASU-topics/set119LPsimplex/nonstand3.pg

    1 ##DESCRIPTION
    2 ##   Evaluation of a simple algebraic expression
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('percent')
    6 
    7 #
    8 # First comes some stuff that appears at the beginning of every problem
    9 #
   10 
   11 DOCUMENT();        # This should be the first executable line in the problem.
   12 
   13 loadMacros(
   14 "PG.pl",
   15 "PGbasicmacros.pl",
   16 "PGchoicemacros.pl",
   17 "PGanswermacros.pl",
   18 "PGauxiliaryFunctions.pl",
   19 "PGmatrixmacros.pl",
   20 "LinearProgramming.pl",
   21 "PGasu.pl"
   22 );
   23 
   24 TEXT(&beginproblem);
   25 install_problem_grader(~~&std_problem_grader);
   26 $showPartialCorrectAnswers=0;
   27 
   28 $r[0] = random(2,10);
   29 for $j (1..4) { do {$r[$j] = random(2,10);} until ($r[$j] != $r[$j-1]);}
   30 
   31 $b = random(5,10);
   32 $a = random(2,5);
   33 
   34 $c = int($b/$a)+ random(1,10);
   35 
   36 $e = random(1,3);
   37 $g = random(1,3);
   38 $f = random(1,2);
   39 do { $f++; } until ($f*$r[1]>$g);
   40 
   41 $fun = nicestring([$e, $f, $g], ['x_1', 'x_2', 'x_3']);
   42 
   43 BEGIN_TEXT
   44 Use the mixed-constraint simplex method to minimize
   45 \[ P = $fun \]
   46 subject to
   47 \[
   48 \begin{array}{rrrrrrr}
   49  $r[0] x_1 & - &  x_2 & - & $r[1] x_3  &\le & - $c \cr
   50  x_1 & + & $a x_2 & + & $r[2] x_3 &\ge & $b \cr
   51  x_1 & - &  x_2 & + & $r[3] x_3 &\le & $r[4] \cr
   52 \end{array}
   53 \]
   54 $BR
   55 \[ x_1 \ge 0\ \qquad x_2  \ge  0 \ \qquad x_3  \ge  0\]
   56   $BR$BR
   57 If there are no solutions, enter $BITALIC None$EITALIC for \(P\).
   58 $BR$BR
   59 \( P = \) \{ans_rule(40)\}
   60 $BR$BR
   61 For the minimum value, enter the values of \(x_1\), \(x_2\), and \(x_3\)
   62 in the spaces provided.  If there are no solutions, you may leave these
   63 answers blank.
   64 $BR$BR
   65 \( x_1 = \) \{ans_rule(40)\}
   66 $BR$BR
   67 \( x_2 = \) \{ans_rule(40)\}
   68 $BR$BR
   69 \( x_3 = \) \{ans_rule(40)\}
   70 END_TEXT
   71 
   72 
   73 
   74 $newsys = [[0, -$r[0], 1, $r[1], -1, 0, 0, $c],
   75 [0, -1-$a*$r[0], 0, $a*$r[1]-$r[2], -$a, 1, 0, -$b+$a*$c],
   76 [0, 1-$r[0], 0, $r[1]+$r[3], -1, 0, 1, $c+$r[4]],
   77 [1, $e+$f*$r[0],  0, $g-$f*$r[1], $f, 0, 0, -$c*$f]];
   78 
   79 for $j (0..3) {
   80  for $k (0..7) {
   81   $newsys->[$j][$k] = new Fraction($newsys->[$j][$k],1);
   82 }}
   83 
   84 ($newsys,$endcode,$pcount) = lp_solve($newsys, fraction_mode=>1);
   85 
   86 $fin0 = lp_current_value(0, $newsys);
   87 $fin0 = ($fin0->times(-1))->print_inline();
   88 $fin1 = lp_current_value(1, $newsys)->print_inline();
   89 $fin2 = lp_current_value(2, $newsys)->print_inline();
   90 $fin3 = lp_current_value(3, $newsys)->print_inline();
   91 
   92 
   93 
   94 ANS(num_cmp($fin0, strings=>['None']));
   95 ANS(num_cmp($fin1));
   96 ANS(num_cmp($fin2));
   97 ANS(num_cmp($fin3));
   98 
   99 ENDDOCUMENT();        # This should be the last executable line in the problem.
  100