The feasible region represented by the given constraints 2 x+3 y 12,-x+ y 3, x 4, y 3 is denoted by

Step-by-step solution

To determine the feasible region satisfying all inequalities, analyze the constraints using boundary lines and the origin as a test point. The inequality 2x + 3y 12 defines the region above the line 2x + 3y = 12 , as the origin (0,0) yields 0 12 . The constraint -x + y 3 corresponds to the region below -x + y = 3 , since (0,0) gives 0 3 . x 4 is satisfied to the left of x = 4 , as 0 4 at the origin. y 3 requires the region above y = 3 , with (0,0) not satisfying 0 3 . Combining these: y 3 eliminates regions S₂ and