Question 104460: hi was wondering if i could get some help with this question please and thank you.
Brook Winfield operates a snowmobile lodge. Last year it had 95 guests, each of which paid $160 per night.The lodge accountant estimates that for every $1 reduction in the price five additional customers will rent a room.
a)write a function representing the revenue of the lodge.
b)what is the maximum projected revenue?
thanks again
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Last year it had 95 guests, each of which paid $160 per night.The lodge accountant estimates that for every $1 reduction in the price five additional customers will rent a room.
a)write a function representing the revenue of the lodge.
b)what is the maximum projected revenue?
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Let "x" be the amount of reduction in price per room below 160.
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Revenue = price * # of guests
Revenue = (160-x)(95+5x)
R(x) = -5x^2+705x+15200
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Maximum occurs when x=-b/2a = -705/(-10) = 70.5
Maximum revenue = R(70.5)
R(70.5) = -5(70.5)^2+705(70.5)+15200
R(70.5) = $40,051.25
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Cheers,
Stan H.
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