Question 18 of 82beginner🔧 ApplyMCQ1 mark

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x² + 36x + 5. The marginal revenue, when x = 15 is

Exercise: EXERCISE 6.1 | Q: 18 | (Page 6)
For More Understanding

Explanation

The context defines marginal revenue as the rate of change of total revenue with respect to the number of items sold. In Example 6, the derivative of the specific function provided in the question (R(x)=3x2+36x+5R(x) = 3x^2 + 36x + 5) is calculated as 6x+366x + 36. Substituting x=15x = 15 into this derivative yields 126126, which matches Option D.

Solution Steps

  1. Step 1: Marginal Revenue is defined as the rate of change of total revenue with respect to the number of units sold. Thus, Marginal Revenue (MR) = dRdx\frac{dR}{dx}.

  2. Step 2: Differentiate the given revenue function R(x)=3x2+36x+5R(x) = 3x^2 + 36x + 5 with respect to xx: MR=dRdx=6x+36MR = \frac{dR}{dx} = 6x + 36.

  3. Step 3: Calculate the marginal revenue at x=15x = 15 by substituting the value in the derivative:

    MR=6(15)+36MR = 6(15) + 36 MR=90+36MR = 90 + 36

    MR=126MR = 126.

  4. Step 4: The marginal revenue is 126. Therefore, the correct option is (D).

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