Question 1026231: Graph the following system of inequalities. 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
2. g ≤ - 3h + 4
g ≥ 3h - 6
g ≥ (⅓)h- 6
f(g, h) = 2g - 3h
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 1. Question 1026330
 <--->
We can graph the boundary lines,
 ,  , and  .
We can find their intersections points (the vertices of the feasible region)
by solving each 2-line system of equations:
 --->
 --->
 ---> .
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  ate each one of those vertices:
 .
The minimum is  .
The maximum is  .
2. I think one of the inequality signs was drawn backwards.
The boundary lines are
 ,  , and  .
  represents the region at or below the red and blue lines, but at or above the green line.
That region is the triangle bound by those lines (including the triangle sides).
The vertices of that triangle are
(0,-6) , (5/3,-1) and (3,-5).
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