Question

constraints of a problem are graphed below. what are the vertices of the feasible region? mark this and the options are: (0, 0), (0, 15), (20, 25), (40, 0); (0, 0), (0, 40), (25, 20), (15, 0); (0, 15), (20, 25), (40, 0); (0, 40), (25, 20), (15, 0)

Explanation:

Step1: Identify x-axis intercepts

The lower boundary hits x-axis at $(40,0)$, left boundary hits x-axis at $(0,0)$.

Step2: Identify y-axis intercepts

The upper left boundary hits y-axis at $(0,15)$, the upper right boundary hits y-axis at $(0,40)$.

Step3: Find intersection of two lines

The two upper lines intersect at $(20,25)$, which is a vertex of the shaded feasible region.

Step4: List all vertices

Compile all corner points of the shaded area: $(0,0)$, $(0,15)$, $(20,25)$, $(40,0)$.

Answer:

(0, 0), (0, 15), (20, 25), (40, 0)