Question

Let P(x,y) = 2x+y Subject to

x+2y≤6
−x+y≤2
x≥0
y≥0
a). Draw the feasible region

Answer 1

To draw the feasible region, plot each inequality's boundary line and shade the area that satisfies all inequalities including x ≥ 0 and y ≥ 0. The feasible region is where the shaded areas overlap, following the constraints given by the problem.

Step-by-step explanation:

The question asks to draw the feasible region for a system of inequalities. To do so, first, plot the boundary lines for each inequality on a graph:

• x + 2y ≤ 6
• −x + y ≤ 2
• x ≥ 0 (this implies that we are considering only the right half of the x-axis)
• y ≥ 0 (this implies that we are considering only the upper half of the y-axis)

After plotting these lines, identify the region that satisfies all of the inequalities simultaneously. This region is called the feasible region. Typically, this is the area where all of the shading overlaps. Each boundary line will be solid, as the inequalities include the equalities as well. Remember to check the points of intersection as potential solutions, and also ensure that the axes' constraints of x ≥ 0 and y ≥ 0 are satisfied. Lastly, label the axes and the function P(x,y), which is subject to these constraints.