Final answer:
To identify the feasible region for a set of constraints, graph and shade the regions that satisfy each inequality, and find the intersection of all shaded regions. The feasible region is the intersection of the shaded regions and the non-negative quadrant.
Step-by-step explanation:
To identify the feasible region for the given set of constraints, we need to graph the inequalities and shade the region that satisfies all the constraints.
First, let's graph the inequality 0.5a + 0.25b ≥ 30. This inequality represents the constraint that 0.5 times the value of a plus 0.25 times the value of b must be greater than or equal to 30. To graph this inequality, we draw the line 0.5a + 0.25b = 30 and shade the region that is below or on the line.
Similarly, we graph the inequalities 1a + 5b ≥ 255 and 0.25a + 0.5b ≤ 55, and shade the regions that satisfy these inequalities. The intersection of all the shaded regions represents the feasible region.
In this case, since a and b must also be greater than or equal to 0, the feasible region is the intersection of the shaded regions and the non-negative quadrant.