Question

The demand function for a certain product is such that\(P(x) = 3x^2 - x + 200\), where \(x\) is the number of units of the product demanded and \(p(x)\) is the price per unit. Marginal revenue when 10 units are sold is:

• A. 59
• B. 780
• C. 1080
• D. 4900

Answer 1

The Correct Option is C

To find the marginal revenue when 10 units are sold, we must first understand that marginal revenue is the derivative of the revenue function with respect to quantity. The revenue function, \(R(x)\), is given by the product of the price function and quantity, \(R(x) = P(x) \cdot x\). First, let's compute \(R(x)\):

\(R(x) = (3x^2 - x + 200) \cdot x = 3x^3 - x^2 + 200x\).

Next, we find the derivative of the revenue function, \(R'(x)\), which gives the marginal revenue:

\(R'(x) = \frac{d}{dx}[3x^3 - x^2 + 200x] = 9x^2 - 2x + 200\).

Now, substitute \(x = 10\) to find the marginal revenue when 10 units are sold:

\(R'(10) = 9(10)^2 - 2(10) + 200 = 900 - 20 + 200 = 1080\).

Therefore, the marginal revenue when 10 units are sold is 1080.