anonymous
  • 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.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
Anyone? I really need help in this one
campbell_st
  • 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
  • anonymous
So how do I find T?
anonymous
  • anonymous
I have to submit this in 15 min, any further help would be greatly appreciated
campbell_st
  • 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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