2. Minimize \( C=3 m+n \) subject to the constraints \( m+n \geq 3,2 m \geq 5, m \geq 0, n \geq 0 \) \[ \begin{array}{l} m+n \geq 3 \\ 2 m \geq 5 \\ m \geq 0 \\ n \geq 0 \end{array} \]

First additional information: To visualize the constraints and the feasible region, you can plot the inequalities on a coordinate system. The line \( m+n=3 \) can be graphed by finding intercepts: when \( m=0 \), \( n=3 \) and when \( n=0 \), \( m=3 \). The second inequality \( 2m=5 \) simplifies to \( m=2.5 \), a vertical line on the graph. Don’t forget the non-negativity constraints, which restrict our values to the first quadrant. This will help you easily identify the corner points where the minimum may occur! Second additional information: Once you've plotted the feasible region, you can evaluate the corners where the constraints intersect. These could be key to your solution. Compute the cost \( C=3m+n \) at each corner point, which could include \( (0,3) \), \( (2.5,0) \), and the intersection of \( m+n=3 \) with \( m=2.5 \), leading to the point \( (2.5,0.5) \). Calculate \( C \) at each point. The smallest value you find will be your minimum cost, giving you an optimal solution to the problem!