1. The problem is to draw the feasible regions for the systems of linear inequalities given in parts a, b, and c. These regions are bounded by lines and axes. 2. Part (a): 2x + y \leq 8, x + y \leq 6, x \geq 0, y \geq 0. - The lines are: $$2x + y = 8$$ $$x + y = 6$$ and the coordinate axes x = 0, y = 0. - To sketch the feasible region, plot these lines and shade the region that satisfies all inequalities simultaneously (below or on these lines and in the first quadrant). 3. Part (b): 3x + 6y \geq 18, 6x + 3y \leq 18, x \geq 0, y \geq 0. - The boundary lines are: $$3x + 6y = 18$$ $$6x + 3y = 18$$ along with x = 0 and y = 0. - The feasible region is where $$3x + 6y \geq 18$$ (above or on the first line) and $$6x + 3y \leq 18$$ (below or on the second line), and also x, y nonnegative. 4. Part (c): x + y \leq 6, 2x + 3y \geq 12, x \geq 2, y \geq 0. - The boundary lines are: $$x + y = 6$$ $$2x + 3y = 12$$ $$x = 2$$ and y = 0. - The feasible region lies below or on the first line, above or on the second line, to the right or on x = 2, and above or on y = 0. 5. To find exact corner points, solve line intersections. For example, in (a) solve - Intersection of $$2x + y = 8$$ and $$x + y = 6$$: Subtract to get $$x = 2$$, then $$y = 4$$. 6. Summarizing: each feasible region is the polygon formed by these lines in the first quadrant, including boundaries. 7. Plotting these on Cartesian coordinates with x-axis horizontal and y-axis vertical will show the required shaded regions representing the solution sets.