Question

Sketch the region that corresponds to the given inequalities. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) 4x + 2y ≥ 4

4x − 2y ≤ 4
x ≥ 0

Answer 1

The region corresponding to the given inequalities is the area above the line 4x+2y=4, below the line 4x−2y=4, and to the right of the y-axis.

Step 1: Graph each inequality individually.

1. 4x + 2y ≥ 4

Rewrite the inequality in slope-intercept form: 2x + y ≥ 2

y-intercept: 2

Slope: 2

Graph the line passing through (0, 2) with a slope of 2. Shade the region above the line (because ≥ is used).

2. 4x - 2y ≤ 4

Rewrite the inequality in slope-intercept form: 2x + y ≥ -2

y-intercept: -2

Slope: 2

Graph the line passing through (0, -2) with a slope of 2. Shade the region below the line (because ≤ is used).

3. x ≥ 0

This inequality is satisfied only for non-negative x-values.

Shade the region to the right of the y-axis (including the y-axis).

Step 2: Identify the feasible region.

The feasible region is the area that satisfies all three inequalities simultaneously. This is the shaded area between the lines x ≥ 0, 2x + y ≥ 2, and 2x + y ≥ -2.

Step 3: Update the graph.

Select the "Update Graph" button to see the feasible region plotted on the screen.