Please explain how they found the cost of the upgrades per 1% of improvement. Is

Question

Please explain how they found the cost of the upgrades per 1% of improvement. Is there a formula?

On a large system, suppose we can upgrade a CPU to make it 50% faster for $10,000 or upgrade its disk drives for $7,000 to make them 150% faster. Processes spend 70% of their time running in the CPU and 30% of their time waiting for disk service. An upgrade of which component would offer the greater benefit for the lesser cost? For the processor option, f = 0.70, k = 1.5, s = 1/(1 - 0.7) + 0.7/1.5 = 1.30 For the disk drive option, f = 0.30, k = 2.5, s = 1/(1 - 0.3) + 0.3/2.5 = 1.22 Each 1% of improvement for the processor costs $333, and for the disk a 1% improvement costs $3.1.8

Explanation / Answer

Given upgraded speed up for processor is 1.30

% of improvement is = (1.3 - 1 ) * 100 = 30 %

Now for 30% of improvement it will cost 10000$

       for 1% of improvement cost will be 10000$ * 1 / 30 = 333.33 = 333 $ (approx)

Hence 1% of improvement for the processor will cost 333 $.

Given upgraded speed up for disk drive 1.22

% of improvement is = (1.22 - 1 ) * 100 = 22 %

Now for 22% of improvement it will cost 7000$

       for 1% of improvement cost will be 7000$ * 1 / 22 = 318.18 = 318 $ (approx)

Hence 1% of improvement for the disk drive will cost 318 $.

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