Assume that both machines have no resale value and future costs are not discounted.

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written 8.4 years ago by

teamques10 ★ 68k

• modified 4.0 years ago

Machine A costs Rs. 45,000 and the operating costs are estimated at Rs. 1,000 for the first year, increasing by Rs. 10,000 per year in the second and subsequent years. Machine B costs Rs. 50,000 and operating costs are Rs. 2,000 for the first year, increasing by Rs. 4,000 per year in the second and subsequent years. If we now have a machine of type A, should we replace it with B? If so, when? Assume that both machines have no resale value and future costs are not discounted. -

operation research

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written 8.4 years ago by

teamques10 ★ 68k

Machine A: Cost (C) = Rs. 45000

Year	Purchase price resale value (C-S)	Running cost	Σ Maintenance costs	Total costs (purchase price resale value + Σ Maintenance costs)	Average annual cost
1	45000	1000	1000	46000	46000
2	45000	11000	12000	57000	28500
3	45000	21000	33000	78000	26000
4	45000	31000	64000	105000	26250

Machine B: Cost (C) = Rs. 50000

Year	Purchase price resale value (C-S)	Running cost	Σ Maintenance costs	Total costs (purchase price resale value + Σ Maintenance costs)	Average annual cost
1	50000	2000	2000	52000	52000
2	50000	6000	8000	58000	29000
3	50000	10000	18000	68000	22666.67
4	50000	14000	32000	82000	20500
5	50000	18000	50000	100000	20000
6	50000	22000	72000	122000	20333.33

Yes, machine A should be replaced with machines B, since the minimum average annual cost of machines B is less than that of machines A.
Since we already have machine A, we should continue operating it till its optimal period, i.e. 3 years, since the annual average cost is minimum. After 3 years, it should be replaced with machine B.

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