A person wants to plant some trees in his community park. The local nursery has to perform this task. It charges the cost of planting trees by the following formula C(x) = x 3 − 45x 2 + 600x, Where x is the number of trees and C(x) is the cost of planting x trees in rupees. The local authority has imposed a restriction that it can plant 10 to 20 trees in one community park for a fair distribution. For how many trees should the person place the order so that he has to spend the least amount? How much is the least amount? Use calculus to answer these questions. Which value is being exhibited by the person?

Download Sample Paper of Class 12 here  https://www.teachoo.com/cbse/sample-papers/

Slide61.JPG

Slide62.JPG
Slide63.JPG Slide64.JPG

 

  1. Class 12
  2. Sample Papers, Previous Year Papers and Other Questions
Ask Download

Transcript

Question 17 A person wants to plant some trees in his community park. The local nursery has to perform this task. It charges the cost of planting trees by the following formula C(x) = x3 − 45x2 + 600x, Where x is the number of trees and C(x) is the cost of planting x trees in rupees. The local authority has imposed a restriction that it can plant 10 to 20 trees in one community park for a fair distribution. For how many trees should the person place the order so that he has to spend the least amount? How much is the least amount? Use calculus to answer these questions. Which value is being exhibited by the person? Given C(x) = x3 − 45x2 + 600x where 10 ≤ x ≤ 20 We have to find minimum value of C(x) Finding C’(x) C’(x) = 3x2 − 45 × 2x + 600 C’(x) = 3x2 − 90x + 600 Putting C’(x) = 0 3x2 − 90x + 600 = 0 3(x2 − 30x + 200) = 0 x2 − 30x + 200 = 0 x2 − 20x – 10x + 200 = 0 x(x − 20) – 10(x – 20) = 0 (x – 20) (x – 10) = 0 So, x = 20, x = 10 We are given interval [10, 20] Hence calculating f(𝑥) at 𝑥 = 10, 20 Hence, Absolute maximum value is 2000 at x = 20 ∴ Person must place order for minimum 20 trees and Least Amount spent = Rs 2000 We are also asked Which value is being exhibited by the person? Here, they are not aksing any mathematical value, they are asking human values like humility, honesty etc. Since the person has less money but still is working for the environment, The trait shown by the person is – caring for healthy environment despite being economically constraint

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail