Maximizing Profit for Widget Production

A manufacturing company produces two types of widgets: Type A and Type B. Each Type A widget requires 2 hours of labor and $4 in materials, while each Type B widget requires 3 hours of labor and $5 in materials. The company has a total of 60 hours of labor available and $100 for materials.

Let x represent the number of Type A widgets produced, and y represent the number of Type B widgets produced. The constraints for labor and material can be modeled by the following inequalities:

• Labor: $$2x + 3y \leq 60$$
• Materials: $$4x + 5y \leq 100$$

If the company wants to maximize its profit of $3 for each Type A widget and $4 for each Type B widget, what is the maximum profit the company can achieve?