Identify the objective function and constraints.

let's maximize this objective function!

Step 1: Identify the objective function and constraints.
The objective function to maximize is $P = 3x + 5y$.
The constraints are:

1. $x - 3y + 5 \le 0 \implies x - 3y \le -5$
2. $2x + y \le 20$
3. $3x + 2y \ge 25$
4. $y < 8$ (We will consider the boundary $y=8$ for finding vertices, and note that the feasible region does not include points where $y=8$)
5. $x \ge