A factory produces two types of items, Item P and Item Q. Each unit of Item P requires $h_P$ hours of machine time, and each unit of Item Q requires $h_Q$ hours of machine time. The total machine time available for production is $T$ hours. The graph representing all possible combinations of units of Item P ($p$) and units of Item Q ($q$) that can be produced with the total available machine time is a line on a coordinate plane. This line passes through the points $(P_{max},0)$ and $(0,Q_{max})$, where $P_{max}$ is the maximum number of Item P that can be produced if no Item Q is produced, and $Q_{max}$ is the maximum number of Item Q that can be produced if no Item P is produced. If $h_Q=3h_P$, what is the value of $\frac{Q_{max}}{P_{max}}$?