City Guilds Model Questions Vol1 2023 Engineering Question 13
Practice objective / multiple choice question 13 from the 2023 City Guilds Model Questions Vol1 Engineering examination.
An equipment component has a constant failure rate of \(\lambda = 0.0002\ \text{h}^{-1}\) (exponential distribution). The cost of replacing the component is \(\₦20{,}000\) and the cost incurred for each hour of equipment downtime is \(\₦5{,}000\). If a preventive replacement is scheduled every \(T\) hours, the average cost per hour is given by\n\[\nC(T)=\frac{20{,}000}{T}+5{,}000 \times 2 \times \bigl(1-e^{-\lambda T}\bigr),\n\]\nwhere the factor \(2\) represents an average downtime of two hours per failure. Determine the value of \(T\) (in hours, to the nearest whole hour) that minimizes the average cost per hour.
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About This Question
This is City Guilds Model Questions Vol1 2023 Engineering Question 13. It is one of the objective questions from the 2023 City Guilds Model Questions Vol1 Engineering examination.
Difficulty level: Hard .
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