Final answer:
To graph the feasible region for the system of inequalities, plot the lines represented by each inequality and find the shaded portion where they overlap. This region is bounded.
Step-by-step explanation:
To graph the feasible region for the system of inequalities, we need to first graph the lines represented by each inequality.
For the inequality x + 4y - 8, we can rewrite it as y = (-1/4)x + 2. This is a linear equation in slope-intercept form, where the slope is -1/4 and the y-intercept is 2. We can plot this line on a coordinate plane.
For the inequality 3x + 4y - 12, we can rewrite it as y = (-3/4)x + 3. This is another linear equation in slope-intercept form, where the slope is -3/4 and the y-intercept is 3. We can plot this line on the same coordinate plane as the first line.
The feasible region is the area where the shaded portions of the two lines overlap. This region is bounded because it is a finite area.