Two alternative options are available for a pump selection in a process unit. The first pump has a unit cost of $$840$ and a Weibull distribution of $=2$ and $=10,000$ hours. The other pump has unit cost of $$870$ and an exponential distribution with an MTTF of $10,000$ hours. The system has an expected lifetime of $15$ years with $2,000$ operating hours per year. It is assumed that any failure in these pumps will result in the same replacement cost. Which pump should be selected based on a $3\%$ interest rate?

$10\%$