Question 16 of 82intermediate🔧 ApplyNumerical4 marks

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 13x² + 26x + 15. Find the marginal revenue when x = 7.

Correct Answer

₹ 208

Exercise: EXERCISE 6.1 | Q: 16 | (Page 5)
For More Understanding

Explanation

This question is from Exercise 6.1, Question 16. It follows the same pattern as Example 6 in the textbook, where marginal revenue is defined as the rate of change of total revenue with respect to the number of items sold at an instant. The student needs to differentiate the revenue function and then substitute x = 7 to find the marginal revenue at that level of output.

Solution Steps

  1. Step 1: Understand the definition - Marginal Revenue (MR) is the rate of change of total revenue with respect to the number of units sold, i.e., MR = dR/dx.

  2. Step 2: Differentiate R(x) - Given R(x) = 13x² + 26x + 15, we have: Marginal Revenue (MR) = dR/dx = 13(2x) + 26(1) + 0 = 26x + 26

  3. Step 3: Substitute x = 7 - When x = 7, MR = 26(7) + 26 = 182 + 26 = 208

  4. Step 4: State the final answer - Hence, the required marginal revenue is ₹ 208.

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