View of /trunk/NationalProblemLibrary/ASU-topics/set119LPsimplex/p9.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 #
   25 # Now we do the randomization of variables, and other computations
   26 # as needed for this problem.  Sometimes we compute the answers here.
   27 #
   28 
   29 $a = random(2,4);
   30 do {$b = random(2,5); } until ($b != $a);
   31 
   32 $d = random(3, 6);
   33 $c = $d+random(1,3);
   34 
   35 $ab = $a*$b;
   36 @c1 = ($c, $d);
   37 @r2 = ($b, $a);
   38 @s = NchooseK(2,2);
   39 @c1 = @c1[@s];
   40 @r2 = @r2[@s];
   41 
   42 BEGIN_TEXT
   43 Use the simplex method to maximize
   44 \[ P = $c1[0] x_1 + $c1[1] x_2 \]
   45 subject to
   46 \[
   47 \begin{array}{rrrrr}
   48 x_1 & + & x_2 & \le & $a \cr
   49 $r2[0] x_1 & + & $r2[1] x_2 & \le & $ab \cr
   50 \end{array}
   51 \]
   52 $BR
   53 \[ x_1 \ge 0\ \qquad x_2  \ge  0 \]
   54   $BR$BR
   55   \( P = \) \{ans_rule(40)\}
   56 END_TEXT
   57 
   58 #
   59 # Tell WeBWork how to test if answers are right.  These should come in the
   60 # same order as the answer blanks above.  You tell WeBWork both the type of
   61 # "answer evaluator" to use, and the correct answer.
   62 #
   63 
   64 ANS(num_cmp($a*$c));
   65 
   66 ENDDOCUMENT();        # This should be the last executable line in the problem.
   67