Question

The shaded region is the solution set of the inequalities

• A. 5x + 4y ≥ 20, x ≤ 6, y ≥ 3, x ≥ 0, y ≥ 0
• B. 5x + 4y ≤ 20, x ≤ 6, y ≤ 3, x ≥ 0, y ≥ 0
• C. 5x + 4y ≥ 20, x ≤ 6, y ≤ 3, x ≥ 0, y ≥ 0
• D. 5x + 4y ≥ 20, x ≥ 6, y ≤ 3, x ≥ 0, y ≥ 0

Answer 1

The Correct Option is C

The inequalities represent a system of constraints defining the shaded region in the graph.
1. \( 5x + 4y \geq 20 \) represents a line that cuts the region into two parts. We are interested in the region above this line.
2. \( x \leq 6 \) represents a vertical line at \( x = 6 \) and restricts the region to the left of this line.
3. \( y \leq 3 \) represents a horizontal line at \( y = 3 \) and restricts the region to below this line.
4. \( x \geq 0 \) and \( y \geq 0 \) ensure that the region is in the first quadrant. Thus, the solution set of the inequalities that defines the shaded region is option (C).

The correct answer is (C) : 5x + 4y ≥ 20, x ≤ 6, y ≤ 3, x ≥ 0, y ≥ 0.