It seems like you want to maximize the objective function $P = 4x + 7y$, but the constraint is not fully clear. Based on your message, it looks like part of the constraint is $3x + y$, but the inequality or equality might be missing.

Please confirm if the constraint is something like:

• $3x + y \leq C$ (where $C$ is some constant)
• $3x + y = C$
• or another form?

Once you clarify, I can proceed with solving the problem for you.