Linear Programming Problem

Answer (a) On

Answer (c) At least one of the corner points

We are asked to find the maximum value of for the given system of inequalities: Step 1: Graph the inequalities - The inequality represents a region below the line . - The inequalities and represent the first quadrant of the coordinate plane. Thus, the feasible region is the triangular region formed by the points where the line intersects the axes, along with the positive x and y axes. Step 2: Find the vertices of the feasible region The line intersects the x-axis at and the y-axis at . The third vertex is the origin . The vertices of the feasible region are , , and . Step 3: Evaluate at each vertex - At , - At , - At , Step 4: Conclusion The maximum value of in the feasible region is , which occurs at the points and . Answer: The maximum value of is , so the correct answer is option (1).