Final answer:
The feasible region is the area on a 2D graph where all constraints overlap. It can be found by graphically plotting the inequalities with A on the x-axis and B on the y-axis, and finding the overlapping area that satisfies all inequalities where A and B are both non-negative.
Step-by-step explanation:
The problem involves identifying the feasible region defined by a set of linear inequalities, which is a typical question in linear programming, a part of mathematics. The constraints are as follows:
- 0.5A + 0.25B >= 30
- 1A + 5B >= 250
- 0.25A + 0.5B <= 50
- A, B >= 0
The feasible region is the area on a graph where all these inequalities overlap and is typically bounded by the lines generated by each inequality equation. To find this region graphically, each inequality should be plotted on a coordinate system with A on the x-axis and B on the y-axis. The area that satisfies all the inequalities simultaneously represents combinations of A and B that meet the given conditions, which includes any points inside the region and the lines of the inequalities themselves, provided they are not strict inequalities (inequalities without the equal to portion). In this case, we're looking for points where A and B are both non-negative, and the inequalities are satisfied, meaning the feasible region will be in the first quadrant of the coordinate system.
To complete the answer, graphing is required, which would show the exact shape and boundaries of the feasible region. To assist the student visually, the tutor would typically draw the graph, highlight the feasible region, and explain how the overlapping shaded areas correspond to the set of possible solutions that satisfy all constraints.