For the following linear inequalities draw the feasibile region
i: x _>1
ii: x+y _<2
iii: x-axis
To draw the feasible region for linear inequalities, we first need to understand what each inequality represents geometrically.
i: x ≥ 1
This inequality means that x should be greater than or equal to 1. Geometrically, this represents all the points on or to the right of a vertical line passing through x = 1.
ii: x + y < 2
This inequality means that the sum of x and y should be less than 2. Geometrically, this represents all the points below the line x + y = 2.
iii: x-axis
This is not an inequality, but rather a reference line. The x-axis is a horizontal line passing through y = 0.
To draw the feasible region, we need to combine the information from all the inequalities.
1. Plot the x = 1 line: Draw a vertical line passing through x = 1.
2. Plot the line x + y = 2: Draw a diagonal line passing through the points (0, 2) and (2, 0). Make sure to make it a dashed line since the inequality is strict (<).
3. The feasible region is the area that satisfies all the given conditions. Therefore, it is the region below the line x + y = 2 and to the right of the line x = 1. Shade this region.
The resulting graph will have the feasible region as the shaded area bounded by the x = 1 line and the dashed line x + y = 2.