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    1 ## DESCRIPTION
    2 ##  Calculus: Optimization Problems
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Optimization Problems')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Differentiation')
   10 ## DBsection('Optimization Problems')
   11 ## Date('5/29/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('4.7')
   18 ## Problem1('29')
   19 
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 0;
   33 
   34 $a = random(2,8,2);
   35 $b = random(2,8,2);
   36 $c = random(380,390,2);
   37 
   38 TEXT(EV2(<<EOT));
   39 The top and bottom margins of a poster are $a cm and the side margins are
   40 each $b cm.  If the area of printed material on the poster is fixed at $c square
   41 centimeters, find the dimensions of the poster with the smallest area.
   42 $PAR
   43 Width = \{&ans_rule(15)\} Height = \{&ans_rule(15)\}
   44 EOT
   45 
   46 $x = ((($b*$c)/$a)**(1/2)) + 2*$b;
   47 $y = ($c/((($b*$c)/$a)**(1/2))) + 2*$a;
   48 
   49 ANS(num_cmp([$x,$y], format=>"%0.5f", relTol=>1));
   50 ENDDOCUMENT();        # This should be the last executable line in the problem.