Suppose that the revenue (in dollars) from the sale of a product is given by , where x is the number of units sold. How fast is the marginal revenue changing when
A) 1.4 dollars per unit
B) -30 dollars per unit
C) 30 dollars per unit
D) -0.1 dollars per unit
E) -1.4 dollars per unit

Question

Suppose that the revenue (in dollars) from the sale of a product is given by  , where x is the number of units sold. How fast is the marginal revenue  changing when  ​
A) 1.4 dollars per unit 
B) -30 dollars per unit 
C) 30 dollars per unit 
D) -0.1 dollars per unit 
E) -1.4 dollars per unit

Quizplus · Accepted Answer

We have,

R(x) = 720x - 0.08x^2

Differentiating both sides w.r.t x, we get

R'(x) = 720 - 0.16x

Now, the marginal revenue is the derivative of the revenue function. Hence, the marginal revenue is given by R'(x).

At x = 2000, we have

R'(2000) = 720 - 0.16(2000)
          = 400

Therefore, the marginal revenue is changing at a rate of -1.4 dollars per unit (decreasing at 1.4 dollars per unit) because the marginal revenue is decreasing as the number of units sold increases. So, the correct answer is (E).

Suppose That the Revenue (In Dollars) from the Sale of a Product