View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework05/stat212-HW05-07.pg

    1 ## DESCRIPTION
    2 ##  Statistics: Probability
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('statistics', 'probability')
    6 ## naw tagged this problem.
    7 
    8 ## DBchapter('Probability')
    9 ## DBsection()
   10 ## Date('6/15/2005')
   11 ## Author('Nolan A. Wages')
   12 ## Institution('UVA')
   13 ## TitleText1('Statistics for Management and Economics')
   14 ## EditionText1('6')
   15 ## AuthorText1('Keller, Warrack')
   16 ## Section1()
   17 ## Problem1()
   18 
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGnumericalmacros.pl",
   28 "PGstatisticsmacros.pl",
   29 "PGauxiliaryFunctions.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 ## install_problem_grader(~~&std_problem_grader);
   35 
   36 $a1 = random(.05,.10,.001);
   37 $a2 = random(.20,.25,.001);
   38 $a3 = random(.30,.40,.001);
   39 $a4 = random(.15,.20,.001);
   40 $a5 = 0.001*floor(1000*(1-($a1+$a2+$a3+$a4))+.5);
   41 $c4 = ((0*$a1)+(1*$a2)+(2*$a3)+(3*$a4)+(4*$a5));
   42 $c5 = random(20,40,1);
   43 $c6 = random(20,30,1);
   44 $c7 = (0.01*$c6);
   45 $c8 = random(10000,20000,1000);
   46 $c9 = random(2,6,.25);
   47 
   48 
   49 BEGIN_TEXT
   50 $PAR
   51 To examine the effectiveness of its four annual
   52 advertising promotions, a mail order company has
   53 sent a questionnaire to each of its customers,
   54 asking how many of the previous year's promotions
   55 prompted orders that would not have otherwise
   56 been made.  The accompanying table lists the
   57 probabilities that were derived from the questionnaire,
   58 where X is the random variable representing the number
   59 of promotions that prompted orders.  If we assume
   60 that overall customer behavior next year will be
   61 the same as last year, what is the expected number
   62 of promotions that each customer will take advantage
   63 of next year by ordering goods that otherwise would
   64 not be purchased?
   65 $PAR
   66 $BCENTER
   67 \{begintable(6)\}
   68 \{row("X", "0", "1", "2", "3", "4",)\}
   69 \{row("P(X)", $a1, $a2, $a3, $a4, $a5)\}
   70 \{endtable()\}
   71 $ECENTER
   72 $PAR
   73 Expected value = \{ans_rule(15)\}
   74 $PAR
   75 A previous analysis of historical records found
   76 that the mean value of orders for promotional
   77 goods is $c5 dollars, with the company earning
   78 a gross profit of $c6$PERCENT on each order.
   79 Calculate the expected value of the profit
   80 contribution next year.
   81 $PAR
   82 Expected value = \{ans_rule(15)\}
   83 $PAR
   84 The fixed cost of conducting the four promotions is
   85 estimated to be $c8 dollars with a variable cost
   86 of $c9 dollars per customer for mailing and handling
   87 costs.  What is the minimum number of customers required by the company
   88 in order to cover the cost of promotions?  (Round your answer to the
   89 next highest integer.)
   90 $PAR
   91 Breakeven point = \{ans_rule(15)\}
   92 $PAR
   93 
   94 
   95 
   96 END_TEXT
   97 
   98 
   99 ANS(num_cmp($c4));
  100 ANS(num_cmp($c5*$c7*$c4));
  101 ANS(num_cmp(1 + floor($c8/(($c5*$c7*$c4)-$c9))));
  102 
  103 
  104 ENDDOCUMENT();       # This should be the last executable line in the problem.