SOLUTION: a motel owner figures he can rent out 50 rooms a night at $100 per night. every time he raises the price by $5, he will rent 2 less rooms. (he will only raise the price by $5 incre

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Question 443310: a motel owner figures he can rent out 50 rooms a night at $100 per night. every time he raises the price by $5, he will rent 2 less rooms. (he will only raise the price by $5 increments.)
a. what price should he set to make the most revenue?
b. how many rooms would he rent (per night) at that rate?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a motel owner figures he can rent out 50 rooms a night at $100 per night. every
time he raises the price by $5, he will rent 2 less rooms. (he will only raise the price by $5 increments.)
:
a. what price should he set to make the most revenue?
Let x = no. of $5 increases, and no. of 2 room decreases
Rev = price per room * no. of rooms rented
R(x) = (100+5x)(50-2x)
FOIL
R(x) = 5000 - 200x + 250x - 10x^2
A quadratic equation
R(x) = -10x^2 + 50x + 5000
axis of symmetry will give us the value of x for max revenue: x = -b/(2a)
x = %28-50%29%2F%282%2A-10%29
x = %28-50%29%2F%28-20%29
x = 2.5
But x has to be an integer, 2 or 3, he raises the price in $5 intervals.
Either he charges $110 a night and rent 46 rooms
or he charges $115 a night and rents 44 rooms
revenue from either DISABLED_event_one= $5060
:
b. how many rooms would he rent (per night) at that rate?
See above