Question

please help on this. suppose the daytime processing load consists of 60% CPU activity and 40% disk activity. Your customers are complaining that the system is slow. After doing some research, you learn that you can upgrade your disks for $8,000 to make them 2.5 times as fast as they are currently. You have also learned that you can upgrade your CPU to make it 1.4 times as fast for $5,000.

1. Which upgrade would you choose that cost the least amount of money per 1% increase in system speed?
2. Which option would you choose if you don’t care about the money, but want a faster system?
3. What is the break-even point for the upgrades? That is, what price would we need to pay for the CPU (but keep the disk cost the same) so the result was the same cost per 1% increase for both?

Answer 1

The fraction of work by CPU (f_CPU): 60%

System Speed increased by Upgraded CPU to Original Speed (k_CPU): 1.4

The fraction of work by DISK (f_DISK): 40%

System Speed increased by Upgraded DISK to Original Speed (k_DISK): 2.5

Speed Up , S_CPU = 1/( (1-f_CPU) + ( f_CPU / k_CPU) ) = 1/((1-0.60)+(0.60/1.4)) = 120.69% 21% faster

S_DISK= 1/( (1-f_DISK) + ( f_DISK / k_DISK) ) = 1/((1-0.40)+(0.40/2.5)) = 131.58% 32% faster

1) Which upgrade would you choose that cost the least amount of money per 1% increase in system speed?

Sol:- I choose CPU Upgrade

because cost per 1% increase in system speed by CPU Upgrade = $5000 / 21 = $238.10.

where as cost per 1% increase in system speed by Disk Upgrade = $8000 / 32  = $250.00

Since, cost per 1% increase in system speed by CPU Upgrade($238.10) is less than cost per 1% increase in system speed by Disk Upgrade($250.00).

Hence, I choose CPU Upgrade.

2)Which option would you choose if you don’t care about the money, but want a faster system?

sol:- I choose DISK Upgrade because DISK Upgrade provides a 32% faster system whereas CPU Upgrade provides only a 21% faster system.

3)What is the break-even point for the upgrades? That is, what price would we need to pay for the CPU (but keep the disk cost the same) so the result was the same cost per 1% increase for both?

sol:-  cost per 1% increase in system speed by Disk Upgrade($250.00) - cost per 1% increase in system speed by CPU Upgrade($238.10).

= $250 - $238.10

=$11.90