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| 1 : | gage | 5 | ## 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 : | jjholt | 480 | ## TitleText1('Calculus: Early Transcendentals') |
| 15 : | ## EditionText1('5') | ||
| 16 : | gage | 5 | ## 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. |
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