document.write( "Question 272692: A manufacture charges $24 for stereo headphones and has been selling about 1000 of them a week. He estimates that for every $1 price reduction, 100 more headphones can be sold per week. What price will maximize the total revenue? \n" ); document.write( "
Algebra.Com's Answer #199549 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A manufacture charges $24 for stereo headphones and has been selling about 1000 of them a week.
\n" ); document.write( " He estimates that for every $1 price reduction, 100 more headphones can be sold per week.
\n" ); document.write( " What price will maximize the total revenue?
\n" ); document.write( ";
\n" ); document.write( "Let x = no. of $1 price reductions and no. of 100 more headphones sold
\n" ); document.write( ";
\n" ); document.write( "R(x) = (24 - x)(1000 + 100x)
\n" ); document.write( "FOIL
\n" ); document.write( "R(x) = 24000 + 2400x - 1000x - 100x^2
\n" ); document.write( ":
\n" ); document.write( "R(x) = 24000 + 1400x - 100x^2
\n" ); document.write( "in standard form
\n" ); document.write( "-100x^2 + 1400x + 24000 = 0
\n" ); document.write( ":
\n" ); document.write( "A quadratic equation; find the axis symmetry which will be the value for x that
\n" ); document.write( " gives max revenue; x = -b/(2a); In this equation; a= -100, b = 1400
\n" ); document.write( "x = \"%28-1400%29%2F%282%2A-100%29\"
\n" ); document.write( "x = +7: no of dollar decreases for max revenue
\n" ); document.write( ";
\n" ); document.write( "24 - 7 = $17 for max revenue
\n" ); document.write( ":
\n" ); document.write( "Find max revenue, substitute 7 for x in the original equation
\n" ); document.write( "R = -100(7^2) + 1400(7) + 24000
\n" ); document.write( "R = -4900 + 9800 + 24000
\n" ); document.write( "R = $28,900
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check: 1700 items * $17 = 28900 \n" ); document.write( "
\n" );