Ex 6.1,18 - Chapter 6 Class 12 Application of Derivatives

Transcript

Ex 6.1,18 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 (A) 116 (B) 96 (C) 90 (D) 126 Since Marginal Revenue is Rate of change in total Revenue w.r.t no of unit sold Let MR = Marginal cost R 𝑥﷯= Total Revenue 𝑥= no. of unit sold So, MR = 𝑑 𝑅 𝑥﷯﷯﷮𝑑𝑥﷯ It is Given that R 𝑥﷯=3 𝑥﷮2﷯+36𝑥+15 We need to find marginal Revenue when 𝑥 = 15 i.e. MR at 𝑥 = 15 MR = 𝑑 𝑅 𝑥﷯﷯﷮𝑑𝑥﷯ MR = 𝑑 3 𝑥﷮2﷯+36𝑥+5﷯﷮𝑑𝑥﷯ MR = 𝑑 3 𝑥﷮2﷯﷯﷮𝑑𝑥﷯+ 𝑑 36𝑥﷯﷮𝑑𝑥﷯+ 𝑑 5﷯﷮𝑑𝑥﷯ MR = 3 𝑑 𝑥﷮2﷯﷯﷮𝑑𝑥﷯+36 𝑑 𝑥﷯﷮𝑑𝑥﷯+0 MR = 3 ×2𝑥+36 MR = 6𝑥+36 MR when 𝑥 = 15 MR = 6 15﷯+36 MR = 90 + 36 MR = 126 Hence Marginal Revenue is Rs. 126 Thus, D is the correct Answer