Final answer:
The feasible region is a quadrilateral area on the Cartesian plane bordered by the lines y ≤ 13-x , y ≤ 10, x ≤ 7, y ≥ 0, and x ≥ 0. Its corner points are (7,6), (13,0), (0,10), and (0,0), which are situated at the intersections of these bounding lines.
Step-by-step explanation:
The system of inequalities provided can be analyzed to determine the feasible region and its corner points. First, each inequality represents a line on the Cartesian plane, and the area that satisfies all inequalities simultaneously is the feasible region.
- y ≤ 13-x
- y ≤ 10
- x ≤ 7
- y ≥ 0
- x ≥ 0
Each inequality can be graphed as follows:
- y ≤ 13-x: a line with a negative slope that crosses the y-axis at 13.
- y ≤ 10: a horizontal line crossing the y-axis at 10.
- x ≤ 7: a vertical line crossing the x-axis at 7.
- y ≥ 0: the x-axis.
- x ≥ 0: the y-axis.
The corner points of this feasible region can be determined by finding the points of intersection of these lines. To find these points, we solve the system of equations created by pairs of inequalities:
- Solving y = 13-x and x = 7 gives us the point (7,6).
- Solving y = 13-x and y = 0 gives us the point (13,0).
- Solving y = 0 and x = 0 gives us the origin (0,0).
- Solving y = 10 and x = 0 gives us the point (0,10).
- Solving y = 10 and x = 7 does not provide a solution within the feasible region since it is outside the intersection of all inequalities.
The corner points of the feasible region are therefore (7,6), (13,0), and (0,10) along with the origin (0,0).