![r(x)=-\frac{1}{50}x^2+14x](/tex.php?f=r(x)=-\frac{1}{50}x^2+14x)
step-by-step explanation:
let's assume
number of candles set =x
price of of x candles =p(x)
we are given
a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week
so, we get point as (200,10)
![x=200,p=10](/tex.php?f=x=200,p=10)
he finds that when he reduces the price by $1, he then sells 50 more candle sets each week
so, we can find slope
![m=-\frac{1}{50}](/tex.php?f=m=-\frac{1}{50})
now, we can use point slope form of line
![p(x)=mx+b](/tex.php?f=p(x)=mx+b)
now, we can plug values
![p(x)=-\frac{1}{50}x+b](/tex.php?f=p(x)=-\frac{1}{50}x+b)
we can use point
![x=200,p=10](/tex.php?f=x=200,p=10)
and find b
![10=-\frac{1}{50}\times 200+b](/tex.php?f=10=-\frac{1}{50}\times 200+b)
![10=-4+b](/tex.php?f=10=-4+b)
![b=14](/tex.php?f=b=14)
now, we can plug it back
and we get
![p(x)=-\frac{1}{50}x+14](/tex.php?f=p(x)=-\frac{1}{50}x+14)
now, we can find revenue
we know that
revenue = price*quantity
so, we get
![r(x)=x\times p(x)](/tex.php?f=r(x)=x\times p(x))
![r(x)=x\times (-\frac{1}{50}x+14)](/tex.php?f=r(x)=x\times (-\frac{1}{50}x+14))
![r(x)=-\frac{1}{50}x^2+14x](/tex.php?f=r(x)=-\frac{1}{50}x^2+14x)