Final answer:
To solve this problem, we use the graphical method to plot the feasible region formed by the constraints and find the vertex with the maximum value of P.
Step-by-step explanation:
The given problem is a linear programming problem which can be solved using the graphical method. We need to maximize the objective function P = 2x + 3y subject to the given constraints:
- 2x + y ≤ 10
- 2x + 3y ≤ 18
- x ≥ 0
- y ≥ 0
To solve this, we plot the feasible region formed by the intersection of the two constraint lines. Then, we find the vertices of this region and evaluate the objective function at those points. The vertex with the maximum value of P will be the solution to the problem.