For the revenue function given by , find the x-value where that is, where the average revenue equals the marginal revenue. (Note: )
B)
C)
D)
E)

Question

For the revenue function given by  , find the x-value where  that is, where the average revenue equals the marginal revenue. (​Note:  ) ​​
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

Average revenue equals total revenue divided by quantity, and marginal revenue is the derivative of total revenue with respect to quantity. 
Setting the two equal, we have:
(14000Q - 0.1Q^2)/Q = 14000 - 0.2Q
14000 - 0.1Q = 14000 - 0.2Q
0.1Q = 0.05 Q
Q = 500
Therefore, the x-value where average revenue equals marginal revenue is 500. Plugging in Q=500 back into the revenue function, we get:
P = 14000 - 0.2(500) = 13000
So the answer is C.

For the Revenue Function Given by , Find the X-Value