##DESCRIPTION
## DBsubject('Algebra')
## DBchapter('Functions')
## DBsection('Modeling with Functions')
## KEYWORDS('word problem','revenue')
## Author('N.Spencer Sitton')
## Institution('NAU')
##ENDDESCRIPTION

# File Created: 06/20/05
# Location: Northern Arizona University
# Course:Quantitative Reasoning

DOCUMENT();     
loadMacros("PGstandard.pl"   
);     

TEXT(&beginproblem);

do{$total1 = random( 800, 1600, 100);
  $total2 = random( 800, 1600, 100);
} until( $total1 > $total2);

do{$price1 = random( 2.05, 2.95, .05);
  $price2 = random( 2.05, 2.95, .05);
  $newprice = random( 2.05, 2.95, .05);
} until( $price1 > $newprice && $newprice > $price2 );

do{$total3 = random( 800, 1600, 100);
} until( $total1 != $total3 || $total2 != $total3 );

$slope = ( $price2 - $price1 ) / ( $total1 - $total2 );
$yint = $price2 - ( $slope * $total1 ) ;

$ans1 = ( $newprice - $yint) / ($slope);
$ans2 = $slope * $total3 + $yint;

$rev1 = ( $price2 ) * ( $total1);
$rev2 = ( $price1 ) * ( $total2);
$rev3 = ( $newprice ) * ( $ans1 );
$rev4 = ( $ans2 ) * ( $total3 );

$max = max( $rev1, $rev2, $rev3, $rev4 );

if( $max == $rev1 ){ $ans3 = $price2 }
elsif( $max == $rev2 ){ $ans3 = $price1 }
elsif( $max == $rev3 ){ $ans3 = $newprice }
elsif( $max == $rev4 ){ $ans3 = $ans2 }

$cval = (-$yint)/(2*$slope);

$ans4 = ( $slope * $cval ) + $yint;

TEXT(
qq!
A gas station sells $total1 gallons of gasoline per hour if it charges
$DOLLAR !,sprintf( "%1.2f", $price2 ), qq! per gallon but only $total2 
gallons per hour if it charges $DOLLAR !,sprintf( "%1.2f", $price1 ), qq! 
per gallon. Assuming a linear model
$PAR

(a) How many gallons would be sold per hour of the price is $DOLLAR
!,sprintf( "%1.2f", $newprice ), qq! per gallon?$BR Answer:!, ans_rule(10),
qq! $PAR

(b) What must the gasoline price be in order to sell $total3 gallons per hour?
$BR Answer: $DOLLAR !, ans_rule(10), qq!
$PAR

(c) Compute the revenue taken at the four prices mentioned in this problem -- 
$DOLLAR !,sprintf( "%6.2f", $price2 ),qq!, $DOLLAR !,sprintf( "%6.2f", $newprice ), 
qq!, $DOLLAR !,sprintf( "%6.2f", $price1 ), qq! and your answer to part (b). 
Which price gives the most revenue? $BR Answer: $DOLLAR !, ans_rule(10) ,qq!
$PAR

(d) What is the price that the gas station should charge to maximize revenue? 
$BR Answer: $DOLLAR !,ans_rule(10) ,qq!
!,
);

ANS( num_cmp( $ans1 ) );
ANS( num_cmp( $ans2 ) );
ANS( num_cmp( $ans3 ) );
ANS( num_cmp( $ans4 ) );

ENDDOCUMENT();