View of /trunk/NationalProblemLibrary/ASU-topics/set119LPsimplex/nonstand1.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 "PGasu.pl"
   20 );
   21 
   22 TEXT(&beginproblem);
   23 
   24 $b = random(2,4);
   25 $b1 = $b+1;
   26 $k = random(3,6);
   27 $a = random($b*$k+1,($b+1)*$k-1);
   28 $f= random(2,4);
   29 $e = $f+random(1,4);
   30 $rr=$b*$b1*$k;
   31 $c=random(2,5);
   32 $rrp = $b1*($a-$b*$k)+$c*$b*($b1*$k-$a);
   33 $rrp = $a if $a>$rrp;
   34 $rrp = $b1*$k if $b1*$k > $rrp;
   35 $rrp += random(1,5);
   36 
   37 
   38 BEGIN_TEXT
   39 Use the mixed-constraint simplex method to maximize
   40 \[ P = $e x_1 + $f x_2 \]
   41 subject to
   42 \[
   43 \begin{array}{rrrrr}
   44  x_1 & + &  x_2 & \ge & $a \cr
   45  $b x_1 & + & $b1 x_2 & \ge & $rr \cr
   46  x_1 & + & $c x_2 & \le & $rrp \cr
   47 \end{array}
   48 \]
   49 $BR
   50 \[ x_1 \ge 0\ \qquad x_2  \ge  0 \]
   51   $BR$BR
   52 If there are no solutions, enter $BITALIC None $EITALIC for \(P\).
   53 $BR$BR
   54 Maximum value is
   55   \( P = \) \{ans_rule(40)\}
   56 $BR$BR
   57 where \(x_1=\) \{ans_rule(40)\}
   58 $BR$BR
   59 and \(x_2=\) \{ans_rule(40)\}
   60 END_TEXT
   61 
   62 ANS(num_cmp($rrp*$e, strings=>['None']));
   63 ANS(num_cmp($rrp, strings=>['None']));
   64 ANS(num_cmp(0, strings=>['None']));
   65 
   66 ENDDOCUMENT();        # This should be the last executable line in the problem.
   67