Answer:
The feasible region, where all three conditions are satisfied, is the shaded area that lies above the line m = 2, below the line m + b = 8, and above the line b > 4.
Explanation:
To represent the situation of having at most 8 hours to spend at the mall and the beach, with a minimum of 2 hours at the mall and more than 4 hours at the beach, we can create a system of inequalities.
Let's represent the number of hours spent at the mall as "m" and the number of hours spent at the beach as "b".
The given conditions can be expressed as:
1. m ≥ 2 (to spend at least 2 hours at the mall)
2. b > 4 (to spend more than 4 hours at the beach)
3. m + b ≤ 8 (to spend at most 8 hours in total)
Graphically, we can represent this system of inequalities on a coordinate plane. We will have m on the x-axis and b on the y-axis. The inequalities can be plotted as follows:
1. The line m = 2 represents the condition of spending at least 2 hours at the mall. This line is vertical and passes through the point (2, 0).
2. The line b > 4 represents the condition of spending more than 4 hours at the beach. This line is horizontal and passes through the point (0, 4). The area above this line satisfies the inequality.
3. The line m + b = 8 represents the condition of spending at most 8 hours in total. This line has a slope of -1 and intercepts the x-axis at (8, 0) and the y-axis at (0, 8). The area below this line satisfies the inequality.
The feasible region, where all three conditions are satisfied, is the shaded area that lies above the line m = 2, below the line m + b = 8, and above the line b > 4.
By graphing the system of inequalities, we can visually determine the possible combinations of hours spent at the mall and the beach within the given constraints.