The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 13{x^2} + 26x + 15$. Find the marginal revenue when $x = 7$.

Q: The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 13{x^2} + 26x + 15$. Find the marginal revenue when $x = 7$.

Explanation: The total revenue (in rupees) from selling $x$ units of a product is given by: \[R(x) = 13x^2 + 26x + 15\] We are asked to find the marginal revenue when $x = 7$.\[\] Marginal revenue is the rate of change of total revenue with respect to the number of units sold, i.e., $MR = \dfrac{dR}{dx}$ \[\] Differentiate $R(x)$: \[\dfrac{dR}{dx} = 13 \cdot 2x + 26 = 26x + 26\] Now substitute $x = 7$: \[MR = 26 \cdot 7 + 26 = 182 + 26 = 208\] Final Answer: The marginal revenue when $x = 7$ is Rs. 208

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Explanation: The total revenue (in rupees) from selling $x$ units of a product is given by:
$$R(x) = 13x^2 + 26x + 15$$

We are asked to find the marginal revenue when $x = 7$.

Marginal revenue is the rate of change of total revenue with respect to the number of units sold, i.e.,

$MR = \dfrac{dR}{dx}$

Differentiate $R(x)$:

$$\dfrac{dR}{dx} = 13 \cdot 2x + 26 = 26x + 26$$

Now substitute $x = 7$:

$$MR = 26 \cdot 7 + 26 = 182 + 26 = 208$$

Final Answer:
The marginal revenue when $x = 7$ is Rs. 208

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