The graph above illustrates the feasible region for the linear programming problem. The feasible region is where the shaded area lies, bounded by the lines representing the constraints:

• The blue line represents the raw material constraint $2x_1 + 3x_2 \leq 60$.
• The red line represents the labor hours constraint $4x_1 + 3x_2 \leq 96$.

Vertices of the Feasible Region

To determine the optimal solution, we evaluate the profit function at the vertices of the feasible region:

1. Intersection of $2x_1 + 3x_2 = 60$ and $4x_1 + 3x_2 = 96$
2. Intersection with the axes (where $x_1 = 0$ and $x_2 = 0$)

Profit Calculation

I can now calculate the profit for each vertex and determine if there is any slack in the solution. Would you like me to proceed with these calculations?

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Here are some questions to consider next:

1. What are the coordinates of the vertices in the feasible region?
2. How do you calculate the intersection points of the two constraints?
3. What is the maximum profit, and at which point is it achieved?
4. Is there any slack in the constraints at the optimal solution?
5. How would the solution change if the available raw material increased to 70 kg?
6. What if the labor hours available decreased to 80 hours per week?
7. How can the firm utilize any slack resources effectively?
8. What are the implications if the profit per unit of product B increases?

Tip: When dealing with linear programming problems, always identify the feasible region first. The optimal solution lies at one of its vertices.