Question 22 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by Teachoo

This question is similar to Chapter 6 Class 12 Application of Derivatives - Ex 6.1

Please check the question here

https://www.teachoo.com/4337/708/Ex-6.1--15---The-total-cost-C(x)--0.007-x3---0.003-x2/category/Ex-6.1/

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Transcript

Question 22 The cost (in rupees) of producing 𝑥 items in factory, each day is given by 𝐶(𝑥)=0.00013𝑥^3+0.002𝑥^2+5𝑥+2200 Find the marginal cost when 150 items are produced.Since Marginal Cost is Rate of change in Total Cost w.r.t No of items produced Let MC be marginal cost So, MC = 𝒅𝑪/𝒅𝒙 Given, Total Cost = C(𝑥) =0.00013𝑥^3+0.002𝑥^2+5𝑥+2200 We need to find MC when 𝑥=150 Putting 𝒙=𝟏𝟓𝟎 MC = 0.00039〖(𝟏𝟓𝟎)〗^𝟐 + 𝟎.𝟎𝟎𝟒 × 𝟏𝟓𝟎+𝟓 MC = 39/100000 × 22500+4/1000 × 150+5 MC = 39/1000 × 225+4/100 × 15+5 MC = 𝟖𝟕𝟕𝟓/𝟏𝟎𝟎𝟎 +𝟔𝟎/𝟏𝟎𝟎 +𝟓 MC = 8.775+0.6+5 MC = 14.375 Hence, the Required Marginal cost is Rs. 14.375

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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