We are interested to produce $P$ in the reaction $A ightarrow P$ using a continuous reactor

We are interested to produce $P$ in the reaction $A \rightarrow P$ using a continuous reactor at $v=240$ liters/ hr with $C_{A_{0}}=3$ moles/liter. However, it is noticed that there is a second reaction $P \rightarrow R$ that can also occur. This undesired reaction produced undesired product $R$. It is found that both reactions are irreversible and first order with $k_{1}=0.45 \mathrm{~min}^{-1}$ and $k_{2}=0.1 \mathrm{~min}^{-1}$. Derive the objective function for finding maximum yield of $P$.