Question

Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints:

a. 3A+2B≤18
b. 12A+8B≥480
c. 5A+10B=200

Answer 1

The graphs of the constraint lines and solutions for the given constraints are shown below.

Step-by-step explanation:

Graphs of Constraint Lines and Solutions:

1. a. The inequality 3A + 2B ≤ 18 represents a shaded region below the line 3A + 2B = 18. The line has a slope of -3/2 and intercepts at (0,9) and (6,0). The feasible solutions lie within or on this shaded region.
2. b. The inequality 12A + 8B ≥ 480 represents a shaded region above the line 12A + 8B = 480. The line has a slope of -3/2 and intercepts at (0,60) and (40,0). The feasible solutions lie within or on this shaded region.
3. c. The equation 5A + 10B = 200 represents a straight line with a slope of -1/2. The line passes through (0,20) and (40,0), and the only feasible solution is the point (40,0).