Answer:
(0, 0), (0, 3), (2, 3), and (5, 0)
Step-by-step explanation:
The constraints of the problem are:
x + y ≤ 5
y ≤ 3
x ≥ 0
y ≥ 0
Then:
Using the second and fourth inequalities we can write:
0 ≤ y ≤ 3
Knowing that the minimum value of y is 0, then if we replace that in the first equation we get:
x + 0 ≤ 5
x ≤ 5
While for the maximum value of y, y = 3, this inequality becomes:
x + 3 ≤ 5
x ≤ 2
Now, the vertexes are the points where both variables take one of their extremes.
Then, we have a vertex at (0, 0) because we have:
x ≥ 0
y ≥ 0
So this is the vertex when both x and y take the minimum value.
When y takes the maximum value y = 3, and x takes the minimum value x = 0, we have the vertex:
(0, 3)
When y takes the maximum value, y = 3, and x takes the maximum value, x = 2, we have the vertex:
(2, 3)
When y takes the minimum value, y = 0, and x takes the maximum value, x = 5, we have the vertex:
(5, 0)
Then the four vertexes are:
(0, 0), (0, 3), (2, 3), and (5, 0)
