In a pharmaceutical production company, formed active pharmaceutical ingredient $($API$)$ is dried using hot air that must contain at least $2\mathrm{.}0\%$ moisture to prevent rapid drying, creating possible side reactions. Since fresh air contains $1\%$ moisture, a part of the air leaving the drier is recycled to achieve $2\mathrm{.}0\%$ moisture. The available blower is rated for $1000lb\frac{m}{h}r.$ To achieve $2\mathrm{.}0\%$ moisture in air, a part of the air leaving the drier is recycled. API is dried from $20\%$ moisture to $5\%$ moisture. The wet air leaving the drier contains $4\%$ moisture. All percentages are on a mass basis. Determine the amount of $($i$)$ product processed, $($ii$)$ wet air recycled, $($iii$)$ purge flow rate, and $($iv$)$ product formed. $($in class$)$