Shade the feasible region for the following three inequalities 1. \( x \geq 1 \) 2. \( y \geq 2 \) 3. \( y \leq-3 x+11 \)

To shade the feasible region for these inequalities, start by graphing each equation. The first inequality \( x \geq 1 \) is a vertical line at \( x = 1 \) and the area to the right is shaded. The second inequality \( y \geq 2 \) corresponds to a horizontal line at \( y = 2 \) with the area above this line shaded. The final inequality \( y \leq -3x + 11 \) involves a line with a slope of -3 and a y-intercept of 11; shade the area below this line. The feasible region will be the area where all three shaded regions overlap. To help visualize this, plot the lines on a coordinate grid. The intersection of the shaded areas represents the set of solutions that satisfy all three inequalities. Make sure to check corner points, as they often provide the best candidates for optimal solutions in linear programming problems!