An LPP has constraints: x + y ≤ 4

Solution

To determine the nature of the feasible region for the given Linear Programming Problem (LPP) constraints, let's analyze each inequality: 1.     x+y≤4: This inequality represents a region below or on the line x+y=4. In the first quadrant (x≥0,y≥0), this region is bounded by the x-axis, the y-axis, and the line x+y=4. 2.     x+y≥6: This inequality represents a region above or on the line x+y=6. In the first quadrant (x≥0,y≥0), this region extends away from the origin. 3.     x≥0: This constraint restricts the feasible region to the right side of or on the y-axis. 4.     y≥0: This constraint restricts the feasible region to the upper side of or on the x-axis. Now, let's consider the intersection of these regions. The first constraint requires that the sum of x and y is less than or equal to 4. The second constraint requires that the sum of x and y is greater than or equal to 6. It is impossible for both x+y≤4 and x+y≥6 to be simultaneously satisfied. There are no values of x and y that can meet both conditions at the same time. Therefore, there is no region in the xy-plane that satisfies all the given constraints simultaneously. Thus, the feasible region is empty.