Question

What are the vertices of the feasible region with constraints 2x+10≥ y, 4x+2≤ y, x≥ 0, y≥ 0 ?

Select all that apply
a. (2,14)
b. (0,0)
c. (0,2)
d. (2,10)
e. (0,10)
f. (4,18)
g. (6,26)

Answer 1

The vertices of the feasible region with the given constraints are (2/3, 14), (0, 2), and (0, 10).

Step-by-step explanation:

The feasible region represents the set of all possible solutions that satisfy the given constraints. To determine the vertices of the feasible region, we need to find the points of intersection between the lines 2x + 10 = y, 4x + 2 = y, x ≥ 0, and y ≥ 0.

By solving the systems of equations:

2x + 10 = 4x + 2 (equation 1)

x = 2/3

y = 14

4x + 2 = y (equation 2)

x = 0

y = 2

x = 0

y = 10

Therefore, the vertices of the feasible region are (2/3, 14), (0, 2), and (0, 10).