A basketball gym is ${140}^{\text{'}}{100}^{\text{'}}{40}^{\text{'}}.$ The $AC$ has been off and, conditions in the room are $100F(db)$ and $70\%($rh$).$ The principal wants $72F(db)$ and $60\%(m)$ by game time. If you have $5$ hours notice to cool the gym down, what would be the required capacity of the system $(10$pts$)?$ Please show your calculations.