Linear Programming

We are given a system of linear inequalities:
1. , 2. , 3. , 4. . We are asked to maximize .
Step 1: Graph the constraints.
We graph the inequalities to find the feasible region.
Step 2: Identify the corner points.
By solving the system of equations, we find the corner points of the feasible region.
Step 3: Calculate at each corner point.
For each corner point, we calculate the value of . The maximum value occurs at and , giving: Thus, the maximum value of is .