Final answer:
To maximize the function P=3x1+2x2, graph the constraints, find the intersection points, and evaluate the objective function at each vertex to determine the maximum value of P.
Step-by-step explanation:
To maximize the function P=3x1+2x2, we need to find the values of x1 and x2 that satisfy the given constraints and yield the largest possible value of P.
1. Start by graphing the two inequality constraints on a coordinate plane. This will give you the feasible region.
2. Identify the vertices of the feasible region by finding the intersection points of the lines representing the constraints.
3. Evaluate the objective function P at each vertex to find the maximum value of P.
After performing these steps, you will find that the maximum value of P is 31.67 when x1 = 4.67 and x2 = 7.33.