To determine the feasible region defined by the inequalities:
1. Non-Negativity Constraints:
The inequalities and restrict our solution to:
- The first quadrant (including both axes)
2. First Inequality Analysis:
For :
- The boundary line is (passes through (4,0) and (0,2))
- The feasible region is above this line
3. Second Inequality Analysis:
For :
- The boundary line is (passes through (3,0) and (0,6))
- The feasible region is below this line
4. Intersection Points:
The vertices of the feasible region are:
- (0,2) - Intersection of and
- (2,2) - Intersection of and
- (3,0) - Intersection of and
- (0,0) is not included as it violates
5. Graphical Representation:
The feasible region is a closed polygon bounded by:
1. The line segment from (0,2) to (2,2)
2. The line segment from (2,2) to (3,0)
3. The x-axis from (3,0) to infinity (but limited by other constraints)
4. The y-axis from (0,2) to infinity (but limited by other constraints)
Final Conclusion:
The feasible region satisfying all given inequalities is a quadrilateral in the first quadrant bounded by the identified constraints.
Therefore, the correct option is .
