
Demand Equation
The price p and the quantity x sold of a certain product obey the demand equation
p=1/3x + 100 0 less then or equal x less then or equal 300
a) Express the revenue R as a function of x.
b) What is the revenue if 100 units are sold?
c) What quantity x maximizes revenue? What is the maximum revenue?
d) What price should the company charge to maximize.
I am not sure how to get the answers. But I have the answers to this question. I am looking for someone to help me work it out. I have about 4 more like this to do. I am hoping someone can show me how to do this one and I can do the rest.
Answers:
a) R(x)=1/3x^2 + 100x
b) $6667
c) 150; $7500
d) $50
robert

a) It looks like Revenue = Price * Quantity (Sound familiar to you? I have never seen this before....)
So Revenue = px
But p = x/3 + 100
So R(x) = x²/3 + 100x
b) It is saying 100 units are sold. So x = 100. You just put this into the equation that you just worked out.
R(100) = 100²/3 + 100x100 = 6667
c) To find out the maximum value the best way is to differentiate the equation and calculate dR/dx
dR/dx = 2x/3 + 100
Then set this equal to zero.
2x/3 + 100 = 0
And you will find that x = 150
For the second part just put 150 back into the the forumla for R(x).
d) To see what price they need, just put the same value of x into the equation for p.
:) Ok?