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When should the machine be replaced?

written 8.4 years ago by teamques10 ★ 68k

•   modified 4.0 years ago

The cost of a machine is Rs. 6,100 and its scrap value is Rs. 100. The maintenance costs found from experience are as follows: -

Year	1	2	3	4	5	6	7	8
Maintenance cost	100	250	400	600	900	1200	1600	2000

When should the machine be replaced? -

operation research

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written 8.4 years ago by teamques10 ★ 68k

•   modified 6.0 years ago

Cost of machine C = Rs. 6100

Year	Resale value (S)	Purchase price resale value (C-S)	Maintenance Cost	Σ Costs	Total costs (purchase price resale value + Σ costs)	Average annual cost
1	100	6000	100	100	6100	6100
2	100	6000	250	350	6350	3175
3	100	6000	400	750	6750	2250
4	100	6000	600	1350	7350	1837.5
5	100	6000	900	2250	8250	1650
6	100	6000	1200	3450	9450	1575
7	100	6000	1600	5050	11050	1578.57
8	100	6000	2000	7050	13050	1631.25

The machine should be replaced after 6 years of use, since the average annual cost is least.

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