SOLUTION: Please help! Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region. 1. x ≤ 2 3x ­ -y ≥

Algebra ->  Graphs -> SOLUTION: Please help! Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region. 1. x ≤ 2 3x ­ -y ≥      Log On


   

Question 1026330: Please help!
Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region.
1. x ≤ 2
3x ­ -y ≥ - ­2
y ≥ x ­ - 2
f(x, y) = 2x - ­ 3y
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x%3C=2
3x-y%3E=-2<--->3x%2B2%3E=y
y%3E=x-2

We can graph the boundary lines,
red%28x=2%29 , blue%28y=3x%2B2%29 , and green%28y=x-2%29 .

We can find their intersections points (the vertices of the feasible region)
by solving each 2-line system of equations:
system%28x=2%2Cy=x-2%29--->highlight%28system%28x=2%2Cy=0%29%29
system%28x=2%2Cy=3x%2B2%29--->highlight%28system%28x=2%2Cy=8%29%29
system%28y=3x%2B2%2Cy=x-2%29--->highlight%28system%28x=-2%2Cy=-4%29%29 .
The function will be minimum at one of those vertices or all along the boundary line that joins two of them.
Same thing goes for the maximum.
So, we calculate the value for f%28x%2C+y%29+=+2x-3y ate each one of those vertices:
f%282%2C+0%29+=+2%2A2-3%2A0=4
f%282%2C+8%29+=+2%2A2-3%2A8=4-24=-20
f%28-2%2C+-4%29+=+2%28-2%29-3%28-4%29=-4%2B12=8 .
The minimum is highlight%28-20%29 .
The maximum is highlight%288%29 .