Sarthaks APP
0 votes
in Statistics by (64.4k points)

A machine costs Rs. 80,000 and the operating cost is estimated to be Rs. 5000 for the first year and increases by Rs. 7000 every year for next five years. Determine the optimum period for replacement of the machine, assuming that the machine has no scrap (Resale) value.

1 Answer

+1 vote
by (59.5k points)
selected by
Best answer

Here the machine cost = P = Rs. 80,000 and since resale value Sn = 0 ; the depreciation (P – Sn) = 80000 for all the years and let Ci be the operating cost. The Average annual cost A(n) = \(\frac{T}{n}\); Where T = Total cost = (P – Sn) + ΣCi and n = no. of years.

Here, Average annual cost A(n) is minimum for n = 5. 

∴ The optimum replacement age is 5 years, 

i.e., the machines should be replaced at the end of 5 years. 

Minimum annual average cost = Rs. 35000

Sarthaks APP

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.