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- anonymous

Multiple Choice:
A high-tech company purchases a new computing system whose initial value is V. The system will depreciate at the rate f = f(t) and will incur maintenance costs at the rate g = g(t), where t is the time measured in months. The company wants to determine the optimal time to replace the system.

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- anonymous

- schrodinger

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- anonymous

- anonymous

Anyone? I really need help in this one

- campbell_st

well the depreciation will be something like
\[D=v(1 - f)^t\]
V= initial value and
f= rate of depreciation
t = number of months...
so if V = $10000 and f = 5% per month... the
After 1 month the value is D = 10000 x (1-0.05) of 10000x0.95...
After 10 months D = 10000 x(1-0.05)^10
the optimum will be the point(s) of intersection of Maintenance costs and and Depreciation
In the graph below I've assumed maintenance is linear
|dw:1327794673018:dw|

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- anonymous

So how do I find T?

- anonymous

I have to submit this in 15 min, any further help would be greatly appreciated

- campbell_st

\[V timesf(t) = V \times(V/17 - (Vt)/578)\]
then since \[V = Vx(v/17 - (Vt)/578)\]
solving \[V/17 = Vt/578\]
Gives t = 34

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