MATH SOLVE

3 months ago

Q:
# The constraints of a problem are listed below. What are the vertices of the feasible region?0, 0), (0, 3), (2, 3), (5, 0)(0, 0), (0, 5), (2, 3), (5, 0)(0, 0), (2, 3), (5, 0)(0, 3), (0, 5), (2, 3)

Accepted Solution

A:

The vertices are the intersections between the lines.

1) line x + y = 5 and y = 3:

y = 3 => x + 3 = 5 => x = 5 - 3 => x = 2

=> vertix = (2,3)

2) line x + y = 5 and y = 0

=> y = 0 => x + 0 = 5 => x = 5

=> vertix = (5,0)

3) line x + y = 5 and x = 0

=> 0 + y = 5 => y = 5

=> (0,5) ------> this is not a vertix because it is above the line y = 3

4) line y = 3 and x-axis

=> vertix = (0,3)

5) x-axis and y-axis => origin => vertix = (0,0)

So, there are four vertices: (0,0), (5,0), (2,3) and (0,3)

Answer: That is the first option:(0, 0), (0, 3), (2, 3), (5, 0)

1) line x + y = 5 and y = 3:

y = 3 => x + 3 = 5 => x = 5 - 3 => x = 2

=> vertix = (2,3)

2) line x + y = 5 and y = 0

=> y = 0 => x + 0 = 5 => x = 5

=> vertix = (5,0)

3) line x + y = 5 and x = 0

=> 0 + y = 5 => y = 5

=> (0,5) ------> this is not a vertix because it is above the line y = 3

4) line y = 3 and x-axis

=> vertix = (0,3)

5) x-axis and y-axis => origin => vertix = (0,0)

So, there are four vertices: (0,0), (5,0), (2,3) and (0,3)

Answer: That is the first option:(0, 0), (0, 3), (2, 3), (5, 0)