$(40$pt$)$ A facility is to be maintained at $25C$ dry bulb temperature $(db)$ and $50\%$ relative humidity. The space is occupied by $30$ persons who each produce $65$ W of sensible heat and $0\mathrm{.}05k\frac{g}{h}$ of moisture $($heat of vaporization, $h_{fg}=2417\mathrm{.}91k\frac{J}{k}g).$ The design requires the use of $100\%$ fresh air. The outdoor air has a temperature and relative humidity of $31C$ and $70\%,$ respectively. Determine $($a$)$ the quantity and the state of the air supplied to the space, $($b$)$ the required capacity of the cooling and dehumidifying equipment, and $($c$)$ the coil sensible heat ratio. Include the psychrometric chart with your solution.