A product requires two sequential machine operations. The first takes $5$ minutes and the defect percentage is $12.$ The second takes $6\mathrm{.}0$ minutes and the defect percentage is $7.$ Assuming $250$ workdays per year and a daily shift of $10$ hours, it is desired to determine the minimum fractional number of machines to manufacture $50,000$ units per year. In another similar plant belonging to the same company, past annual data on identical operations and working conditions indicate that $10$ machines were out of production a total number of $2198$ hours due to setup and $2052$ hours due to machine unavailability $($for instance, maintenance needs$).$