Final answer:
To graph the constraint lines and solutions, plot each constraint equation as a line on the coordinate plane and shade the regions that satisfy each constraint.
Step-by-step explanation:
To graph the constraint lines and solutions, we need to plot each constraint equation on a coordinate plane.
1. The first constraint is 3a + 2b ≤ 18. We can start by solving this equation for b to get b ≤ (18 - 3a) / 2. Now we can plot this line on the coordinate plane using a few points. For example, when a = 0, b = 9, and when a = 6, b = 0. Connect these points to draw the line. Shade the region below the line to represent the solutions that satisfy this constraint.
2. The second constraint is 12a + 8b ≥ 480. Again, solving for b, we get b ≥ (480 - 12a) / 8. Plot a few points, such as (0, 60) and (40, 0), and connect them to draw the line. Shade the region above the line to represent the solutions that satisfy this constraint.
3. The third constraint is 5a + 10b = 200. We can rearrange this equation to get b = (200 - 5a) / 10. Plot a few points like (0, 20) and (40, 15), and draw the line connecting them. This line represents the solutions that satisfy the equation exactly, so there is no shading needed.
Finally, label each line and shading region appropriately to complete the graph of the constraint lines and solutions.