Ex 6.1,16

Transcript

Ex 6.1,16 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. Since marginal revenue is the rate of change in total cost w.r.t no of units sold Let MR be the marginal revenue & R 𝑥﷯ is total Revenue & 𝑥 is no of units sold So, MR = 𝑑 𝑅 𝑥﷯﷯﷮𝑑𝑥﷯ It is Given that R 𝑥﷯=13 𝑥﷮2﷯+26𝑥+15 We need to find marginal Revenue when 𝑥=7 i.e. MR when 𝑥=7 MR = 𝑑 𝑅 𝑥﷯﷯﷮𝑑𝑥﷯ MR = 𝑑 13 𝑥﷮2﷯+26𝑥+15﷯﷮𝑑𝑥﷯ MR = 𝑑 13 𝑥﷮2﷯﷯﷮𝑑𝑥﷯+ 𝑑 26𝑥﷯﷮𝑑𝑥﷯+ 𝑑 15﷯﷮𝑑𝑥﷯ MR = 13 𝑑 𝑥﷮2﷯﷯﷮𝑑𝑥﷯+26 𝑑 𝑥﷯﷮𝑑𝑥﷯+0 MR = 13 × 2𝑥+26 MR = 26𝑥+26 MR = 26 𝑥+1﷯ We need to find MR when 𝑥=7 Putting 𝑥=7 MR = 26 7+1﷯ MR = 26 × 8 MR = 208 Hence Required marginal Revenue is Rs 208 when 𝒙=𝟕