SOLUTION: Help is very, very much appreciated! I need to understand this problem but do not want just the answer, please. I would like to understand the concept and would appreciate learni

Algebra ->  Expressions-with-variables -> SOLUTION: Help is very, very much appreciated! I need to understand this problem but do not want just the answer, please. I would like to understand the concept and would appreciate learni      Log On


   

Question 334316: Help is very, very much appreciated! I need to understand this problem but do not want just the answer, please. I would like to understand the concept and would appreciate learning how to solve the following problem.
A company sells an item for x dollars each. The monthly revenue for this model is given by the formula R(x)=-0.08x^2 + 300x. Revenue is the product of the price x and the demand (quantity sold). I need to factor out the price on the right-hand side of the formula. Then, write a formula D(x) for the monthly demand. and find D(3000).
Thank you, kindly.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A company sells an item for x dollars each.
The monthly revenue for this model is given by the formula R(x)=-0.08x^2 + 300x.
Revenue is the product of the price x and the demand (quantity sold).
I need to factor out the price on the right-hand side of the formula.
:
We know the price = x, therefore:
:
R(x) = -0.08x^2 + 300x
Factor out x
R(x) = x(-0.08x + 300)
:
"write a formula D(x) for the monthly demand."
The qty sold (Demand) will be the total (Revenue) divided by the price (x)
therefore
D(x) = %28x%28-0.08x+%2B+300%29%29%2Fx
Cancel x
D(x) = -0.08x + 300 is the demand function
:
"and find D(3000)".
x = 3000, therefore
D(3000) = -0.08(3000) + 300
D(3000) = -240 + 300
D(300) = 60 is the demand
:
:
Did this shed some light on your understanding of this??