assistance needed: Express the revenue R as a function of x

[mikey3891]

OK guys this question has been plaguing me all night. any takers.

The price "p" and quantity "x" sold of a certain product obey the demand curve
p= -1/3x + 100, 0 ≤ X ≤ 300

Express the revenue R as a function of x
What is the revenue if 100 units are sold?
What quantity x will maximize revenue? What is the maximum revenue?
What price should the company charge to maximize revenue?

 

[JeffM]

OK guys this question has been plaguing me all night. any takers.

The price "p" and quantity "x" sold of a certain product obey the demand curve
p= -1/3x + 100, 0 ≤ X ≤ 300

Express the revenue R as a function of x
What is the revenue if 100 units are sold?
What quantity x will maximize revenue? What is the maximum revenue?
What price should the company charge to maximize revenue?

Because you have shown no work, we do not know, indeed cannot know, what has been plaguing you. Let's start with the very first question.

Given that price per unit is x and that the quantity sold at that unit price is \(\displaystyle -\dfrac{1}{3} * x + 100\)

what is the revenue realized at unit price x? Any ideas at all?