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.
Marginal revenue is rate of change of total revenue w. r. t the number of unit sold
Let MR be marginal revenue
So, MR = 𝒅𝑹/𝒅𝒙
Given,
Total revenue = R(𝑥)=13𝑥^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(13𝑥^2 + 26𝑥 + 15))/𝑑𝑥
MR = 𝑑(13𝑥^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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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