View of /trunk/NationalProblemLibrary/Rochester/setVmultivariable7MaxMin/ur_vc_7_6.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('minimum' 'triangle' 'multivariable' 'surface area')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Differentiation')
   10 ## DBsection('Optimization Problems')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT();   # This should be the first executable line in the problem.
   22 
   23 loadMacros("PG.pl",
   24            "PGbasicmacros.pl",
   25            "PGchoicemacros.pl",
   26            "PGanswermacros.pl",
   27            "PGauxiliaryFunctions.pl"
   28           );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(2, 20, 1);
   34 $v = $a**3;
   35 
   36 BEGIN_TEXT
   37 You are to manufacture a rectangular box with 3 dimensions x, y and z, and
   38 volume \( v = $v \).  Find the dimensions which minimize the surface area
   39 of this box. $BR
   40 
   41 x = \{ ans_rule(5) \} $BR
   42 y = \{ ans_rule(5) \} $BR
   43 z = \{ ans_rule(5) \} $BR
   44 
   45 END_TEXT
   46 
   47 ANS(num_cmp( $a ) );
   48 ANS(num_cmp( $a ) );
   49 ANS(num_cmp( $a ) );
   50 
   51 
   52 ENDDOCUMENT();    # This should be the last executable line in the problem.