From first reaction: \( A + 2B \rightarrow P_1 \), limiting reagent is B. From second: \( 2P_1 + 3C \rightarrow P_2 \), C is the limiting reagent. Since all of \( P_1 \) reacts completely with C to give \( P_2 \), and since C gets fully used up, \( P_2 \) gets completely consumed too.