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Question 666312: A motel advertises that it will provide dinner, dancing, and drinks for $60 per couple at a New Year's Eve party. It must have a guarantee of 50 couples. Furthermore, it will agree that for each couple in excess of 50, it will reduce the price per couple for all attending by $0.25. How many couples will it take to maximize the motel's revenue?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A motel advertises that it will provide dinner, dancing, and drinks for $60 per couple at a New Year's Eve party. It must have a guarantee of 50 couples. Furthermore, it will agree that for each couple in excess of 50, it will reduce the price per couple for all attending by $0.25. How many couples will it take to maximize the motel's revenue?
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let x=number of couples to maximize motel's revenue
x-50=number of couples in excess of 50
.25(x-50)=reduction in price per couple
Price per couple=[60-.25(x-50)]
Revenue=number of couples*price per couple
y=x[60-(.25(x-50)]
=x[60-.25x+12.5]
=x[-.25x+72.5]
=-.25x^2+72.5x
complete the square
y=-.25(x^2-290+145^2)+.25*145^2
y=-.25(x-145)^2+5256.25
This is a parabola that opens downwards with a maximum of 5256.25 at x=145
How many couples will it take to maximize the motel's revenue=145
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