SOLUTION: 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 so

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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 so      Log On


   

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?
Thanks so much in advance:)
Answer by lwsshak3(11628) About Me  (Show Source):
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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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let x=number of $25 decreases in price
revenue=price*quantity
R=(500-25x)(30+3x)
=15000-750x+1500x-75x^2
=15000-750x-75x^2
=-75x^2+750x+15000
divide by 75
=-x^2+10x+200
complete the square:
=-(x^2-10x+25)+25+200
R=-(x-5)^2+225
This is an equation of a parabola that opens down.
its vertex:(5,225)
number of $25 decreases in price=5
price should she sell the clubs to maximize the income=500-5*25=$375