Final answer:
To find the feasible region for this system of inequalities, graph each inequality and shade the area that satisfies all the conditions. The feasible region is the region below the lines y ≤ 18 - (1/2)x and y ≤ 15, and within the rectangle formed by x ≤ 16 and y ≥ 0. The corner points of this feasible region are (0, 0), (0, 15), (16, 0), and (8, 10).
Step-by-step explanation:
To find the feasible region for this system of inequalities, we need to graph each inequality and shade the area that satisfies all the conditions. Let's start by graphing y ≤ 18 - (1/2)x.
When we graph y ≤ 18 - (1/2)x, we get a line with a slope of -1/2 and y-intercept of 18. We shade below this line to represent y ≤ 18 - (1/2)x.
Next, let's graph y ≤ 15. We get a horizontal line at y = 15, and we shade below this line as well.
Finally, let's graph x ≤ 16 and y ≥ 0. We get vertical and horizontal lines, respectively, forming a rectangle in the first quadrant.
The feasible region is the shaded area where all the inequalities overlap. It is the region below the lines y ≤ 18 - (1/2)x and y ≤ 15, and within the rectangle formed by x ≤ 16 and y ≥ 0.
The corner points of this feasible region are (0, 0), (0, 15), (16, 0), and (8, 10).