View of /trunk/NationalProblemLibrary/ASU-topics/set119LPsimplex/p8piv.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 "LinearProgramming.pl",
   20 "PGmatrixmacros.pl",
   21 "PGasu.pl"
   22 );
   23 
   24 
   25 TEXT(&beginproblem);
   26 $showPartialCorrectAnswers=0;
   27 install_problem_grader(~~&std_problem_grader);
   28 
   29 $tops2 = ['P', 'x_1', 'x_2', 'x_3', 's_1', 's_2', 's_3', '\mbox{\tiny{RHS}}'];
   30 
   31 @base = (1,2,3,4,5,6,7,8,9,10);
   32 
   33 $a = random(-2, -10);
   34 $b = $a - random(3, 7);
   35 $bb = $b - random(3, 10);
   36 $r1 = random(15, 45);
   37 $r2 = random(15, 80);
   38 $a1=random(2,20);
   39 do {$a2 = random(2,20);} until ($a2*$r1 != $a1*$r2) ;
   40 
   41 $sys1 = [
   42 [0, $a1, -random(2,20), random(20,20), 1, 0, 0, $r1],
   43 [0, -random(2,20), random(2,20), -random(2,20), 0, 1, 0,random(15, 80)],
   44 [0, $a2, 0, -random(2,20), 0, 0, 1,$r2],
   45 [1, $bb, $b, $a, 0, 0, 0,random(20, 200)]];
   46 
   47 @sl1 = (0, 4,1,6,3,2, 5, 7);
   48 @ans1 = (0, 0, 0, $sys1->[0][5], $sys1->[1][5],$sys1->[2][5]);
   49 @ans1=@ans1[@sl1];
   50 for $jj (0..3) {
   51   $sys1->[$jj] = [ @{$sys1->[$jj]}[@sl1] ];
   52 }
   53 
   54 ($r, $c) = lp_pivot_element($sys1);
   55 
   56 BEGIN_TEXT
   57 Determine the correct pivot element for the following simplex tableau.
   58 
   59   $BR$BR
   60 \[\{ lp_display_mm($sys1, top_labels=>$tops2) \} \]
   61 $BR$BR
   62 Pivot row number (1, 2, 3, or 4) = \{ ans_rule(10) \}
   63 $BR
   64 Pivot column number (1, 2, ... or 8) = \{ ans_rule(10) \}
   65 END_TEXT
   66 
   67 #
   68 # Tell WeBWork how to test if answers are right.  These should come in the
   69 # same order as the answer blanks above.  You tell WeBWork both the type of
   70 # "answer evaluator" to use, and the correct answer.
   71 #
   72 
   73 ANS(num_cmp($r+1));
   74 ANS(num_cmp($c+1));
   75 
   76 
   77 
   78 ENDDOCUMENT();        # This should be the last executable line in the problem.