1. The problem statement, all variables and given/known data A system is to be operated 5000 hours per year, where Total Cost (for 5 years) = Acquisition cost + Spares cost + Downtime cost System acquisition cost is related to MTBF, θ, as follows: CA(θ) = 685.2917e0.003779θ The average cost of a spare item is $1,000 and the average cost of downtime associated with failure is $5,000. 2. Relevant equations Find MTBF or θ required for a system that will result in approximate minimum total cost over a five-year period if the 3. The attempt at a solution This is my attempt but not sure Find θ = MTBF 1/MTBF = R/T where R= rate of failure and T= total time = 5000hrs => MTBF =T/R = 5000/R Total Cost = Acquisition cost + Spares cost + Downtime cost = 685.2917e^0.003779(5000/R) + 5000R + 1000R = 685e^20/R + 6000R I need to find R such that it will minimize Total Cost and I am stuck. Please check if my approach is correct. Thanks.