document.write( "Question 536681: A caterer in quoting the charge for producing a dinner proposes the following terms. For a group of 60 people, he will charge $30 per person. For every extra 10 people, he will lower the price for $1.50 per person for the whole group. What size group does the caterer want to maximize his income?\r
\n" ); document.write( "\n" ); document.write( "Thanks! \n" ); document.write( "

Algebra.Com's Answer #352659 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
A caterer in quoting the charge for producing a dinner proposes the following terms.
\n" ); document.write( " For a group of 60 people, he will charge $30 per person.
\n" ); document.write( " For every extra 10 people, he will lower the price for $1.50 per person for the whole group.
\n" ); document.write( " What size group does the caterer want to maximize his income?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of groups of 10, that will maximize income
\n" ); document.write( "Let x = no. of $1.50 reductions in price
\n" ); document.write( "Let R = his income
\n" ); document.write( ";
\n" ); document.write( "R = (60+10x)(30 - 1.50x)
\n" ); document.write( "FOIL
\n" ); document.write( "R(x) = 1800 - 90x + 300x - 15x^2
\n" ); document.write( "R(x) = -15x^2 + 210x + 1800
\n" ); document.write( "Find the axis of symmetry
\n" ); document.write( "x = $\"%28-210%29%2F%282%2A-15%29\"$
\n" ); document.write( "x = $\"%28-210%29%2F%28-30%29\"$
\n" ); document.write( "x = +7 groups of 10, 70 more people which would be 130 total
\n" ); document.write( ":
\n" ); document.write( "Cost per person then, 30 - 7(1.50) = $19.50
\n" ); document.write( ":
\n" ); document.write( "Total income: 19.50 * 130 = $2,535 \n" ); document.write( "

\n" );