mimi8734
17.10.2019 •
Mathematics
Acarpet cleaning business has 100 customers when they charge $125 for a cleaning. research shows that every $5 reduction in price attracts another 20 customers. what price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90
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Ответ:
(125,100) and (120,120), from these we can find the slope or rate of change of customers as a function of price...
m=20/-5
m=-4
m=-4
c(p)=-4p+b, now we can use (125,100) to solve for b
100=-4(125)+b
100=-500+b
600=b, so our number of customers as a function of price is:
c(p)=600-4p
Revenue will simply be the number of customers times the price charged per customer...or p*c(p):
r(p)=600p-4p^2
We can find price that creates maximum revenue by finding when the derivative is equal to zero...
dr/dp=600-8p
dr/dp=0 only when
0=600-8p
8p=600
p=75
So the price that maximizes revenue is $75.
Ответ:
all but the middle
Step-by-step explanation:
did this on a test an got 100%