The problem you've uploaded is a linear programming (LP) problem with two variables $x_1$ and $x_2$. You are asked to solve it graphically.

Objective Function:

Maximize $P = 4x_1 + 1x_2$

Constraints:

1. $2x_1 + 4x_2 \leq 24$ (Resource A)
2. $6x_1 + 3x_2 \leq 36$ (Resource B)
3. $x_1 \leq 5$ (Resource C)
4. $2x_2 \leq 10$ (Resource D)
5. $x_1, x_2 \geq 0$ (Non-negativity constraints)

Steps to Solve Graphically:

1. Plot the constraints:

   • Each inequality represents a line on the graph, and the feasible region is the intersection of the half-planes defined by these inequalities.

2. Determine the feasible region:

   • Identify where all the constraints overlap. This is the set of all points that satisfy all inequalities simultaneously.

3. Find the corner points:

   • The maximum (or minimum) of the objective function in a linear program occurs at a corner point (vertex) of the feasible region.

4. Evaluate the objective function at each corner point:

   • Once the corner points are identified, substitute them into the objective function $P = 4x_1 + 1x_2$ to find the value of $P$ at each corner.

5. Select the maximum value:

   • The maximum value of $P$ at any of the corner points is the solution to the linear programming problem.

Let me help you with the graph setup and determining the corner points step by step.

Would you like me to calculate the corner points and evaluate the objective function at these points now?