Final answer:
The student is tasked with graphing linear constraints on a coordinate plane, shading the feasible region that satisfies all inequalities, and identifying the extreme points where these constraints intersect.
Step-by-step explanation:
The student is asked to sketch the feasible region based on a set of linear constraints and identify the extreme points where the inequalities intersect. To solve the problem, each inequality needs to be graphed as a straight line on the coordinate plane. Here are the steps:
- Graph the inequalities as individual lines by finding the intercepts and the slope of each line. Consider the inequality as an equation to plot the line.
- For each inequality, determine which side of the line represents the solution set, this is often done by selecting a test point and substituting it into the inequality.
- Shade the area that satisfies each inequality.
- The feasible region is where all the shaded areas overlap, and it should be clearly marked. This region represents all possible solutions that satisfy all the constraints together.
- Identify the corner points (extreme points) of the feasible region, as these are potential solutions to the problem. These points are typically where the lines intersect and often include the intercepts if they are part of the feasible region.
Sketching the feasible region and identifying the extreme points will visually represent all the combinations of x₁ and x₂ that meet the given constraints while keeping x₁, x₂ ≥0.