Solution: A high-tech company purchases a new computing system whose initial value is

Chapter 5, Problem 32

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A high-tech company purchases a new computing system whose initial value is . The system will depreciate at the rate and will accumulate maintenance costs at the rate , where is the time measured in months. The company wants to determine the optimal time to replace the system. (a) LetShow that the critical numbers of occur at the numbers where . (b) Suppose thatandDetermine the length of time for the total depreciation to equal the initial value . (c) Determine the absolute minimum of on . (d) Sketch the graphs of and in the same coordinate system, and verify the result in part (a) in this case.

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