document.write( "Question 813450: A gold club operator finds that she can sell 30 sets of golf clubs at $500 per set in a year. She predicts that for each $25 the decrease in price 3 extra sets of clubs could be sold. At what price should she sell the clubs to maximize the income?\r
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Algebra.Com's Answer #489751 by lwsshak3(11628)\"\" \"About 
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A gold club operator finds that she can sell 30 sets of golf clubs at $500 per set in a year. She predicts that for each $25 the decrease in price 3 extra sets of clubs could be sold. At what price should she sell the clubs to maximize the income?
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\n" ); document.write( "let x=number of $25 decreases in price
\n" ); document.write( "revenue=price*quantity
\n" ); document.write( "R=(500-25x)(30+3x)
\n" ); document.write( "=15000-750x+1500x-75x^2
\n" ); document.write( "=15000-750x-75x^2
\n" ); document.write( "=-75x^2+750x+15000
\n" ); document.write( "divide by 75
\n" ); document.write( "=-x^2+10x+200
\n" ); document.write( "complete the square:
\n" ); document.write( "=-(x^2-10x+25)+25+200
\n" ); document.write( "R=-(x-5)^2+225
\n" ); document.write( "This is an equation of a parabola that opens down.
\n" ); document.write( "its vertex:(5,225)
\n" ); document.write( "number of $25 decreases in price=5
\n" ); document.write( "price should she sell the clubs to maximize the income=500-5*25=$375
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