Question

The total revenue in Rupees received from the sale of \( x \) units of a product is given by \( R(x) = 3x^2 + 36x + 5 \). The marginal revenue, when \( x = 15 \), is _____

• A. \( 116 \)
• B. \( 90 \)
• C. \( 96 \)
• D. \( 126 \)

Hint:

Marginal value = derivative evaluated at given point.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Marginal Revenue ($MR$) is the rate of change of total revenue with respect to the number of units sold. Mathematically, $MR = \frac{dR}{dx}$.
Step 2: Formula Application:
$R(x) = 3x^2 + 36x + 5$ $MR = \frac{d}{dx}(3x^2 + 36x + 5) = 6x + 36$.
Step 3: Explanation:
Substitute $x = 15$ into the marginal revenue function: $MR = 6(15) + 36$ $MR = 90 + 36 = 126$.
Step 4: Final Answer:
The marginal revenue is 126.