View of /branches/NAU/setLinearModeling/linearmodeling2_alt.pg

    1 ##DESCRIPTION
    2 ## DBsubject('Algebra')
    3 ## DBchapter('Functions')
    4 ## DBsection('Modeling with Functions')
    5 ## KEYWORDS('word problem','revenue')
    6 ## Author('N.Spencer Sitton')
    7 ## Institution('NAU')
    8 ##ENDDESCRIPTION
    9 
   10 # File Created: 06/20/05
   11 # Location: Northern Arizona University
   12 # Course:Quantitative Reasoning
   13 
   14 DOCUMENT();
   15 loadMacros("PGstandard.pl"
   16 );
   17 
   18 TEXT(&beginproblem);
   19 
   20 do{$total1 = random( 800, 1600, 100);
   21   $total2 = random( 800, 1600, 100);
   22 } until( $total1 > $total2);
   23 
   24 do{$price1 = random( 2.05, 2.95, .05);
   25   $price2 = random( 2.05, 2.95, .05);
   26   $newprice = random( 2.05, 2.95, .05);
   27 } until( $price1 > $newprice && $newprice > $price2 );
   28 
   29 do{$total3 = random( 800, 1600, 100);
   30 } until( $total1 != $total3 || $total2 != $total3 );
   31 
   32 $slope = ( $price2 - $price1 ) / ( $total1 - $total2 );
   33 $yint = $price2 - ( $slope * $total1 ) ;
   34 
   35 $ans1 = ( $newprice - $yint) / ($slope);
   36 $ans2 = $slope * $total3 + $yint;
   37 
   38 $rev1 = ( $price2 ) * ( $total1);
   39 $rev2 = ( $price1 ) * ( $total2);
   40 $rev3 = ( $newprice ) * ( $ans1 );
   41 $rev4 = ( $ans2 ) * ( $total3 );
   42 
   43 $max = max( $rev1, $rev2, $rev3, $rev4 );
   44 
   45 if( $max == $rev1 ){ $ans3 = $price2 }
   46 elsif( $max == $rev2 ){ $ans3 = $price1 }
   47 elsif( $max == $rev3 ){ $ans3 = $newprice }
   48 elsif( $max == $rev4 ){ $ans3 = $ans2 }
   49 
   50 $cval = (-$yint)/(2*$slope);
   51 
   52 $ans4 = ( $slope * $cval ) + $yint;
   53 
   54 TEXT(
   55 qq!
   56 A gas station sells $total1 gallons of gasoline per hour if it charges
   57 $DOLLAR !,sprintf( "%1.2f", $price2 ), qq! per gallon but only $total2
   58 gallons per hour if it charges $DOLLAR !,sprintf( "%1.2f", $price1 ), qq!
   59 per gallon. Assuming a linear model
   60 $PAR
   61 
   62 (a) How many gallons would be sold per hour of the price is $DOLLAR
   63 !,sprintf( "%1.2f", $newprice ), qq! per gallon?$BR Answer:!, ans_rule(10),
   64 qq! $PAR
   65 
   66 (b) What must the gasoline price be in order to sell $total3 gallons per hour?
   67 $BR Answer: $DOLLAR !, ans_rule(10), qq!
   68 $PAR
   69 
   70 (c) Compute the revenue taken at the four prices mentioned in this problem --
   71 $DOLLAR !,sprintf( "%6.2f", $price2 ),qq!, $DOLLAR !,sprintf( "%6.2f", $newprice ),
   72 qq!, $DOLLAR !,sprintf( "%6.2f", $price1 ), qq! and your answer to part (b).
   73 Which price gives the most revenue? $BR Answer: $DOLLAR !, ans_rule(10) ,qq!
   74 $PAR
   75 
   76 !,
   77 );
   78 
   79 ANS( num_cmp( $ans1 ) );
   80 ANS( num_cmp( $ans2 ) );
   81 ANS( num_cmp( $ans3 ) );
   82 
   83 
   84 ENDDOCUMENT();