Question 278813: I am having trouble with this problem. I need to determine if the graph is bounded and what the corner points are. Can you please help me find the corner points? Thank you.
x + y _>_ 1
2x + 3y _<_ 12
3x + y _<_ 9
x _>_ 0
y _>_0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I am having trouble with this problem. I need to determine if the graph is bounded and what the corner points are. Can you please help me find the corner points? Thank you.
x + y _>_ 1
2x + 3y _<_ 12
3x + y _<_ 9
x _>_ 0
y _>_0
------------------
The last two inequalities put the graphs in the 1st quadrant.
---
Graph y = -x+1; shade the half-plane above the line
Graph y = (-2/3)x + 4 ; shade the half-plane below the line
Graph y = -3x+9 ; shade the half-plane below the line
------------------------------------------------
----
Look at those results to see if you have a closed area in the 1st Quadrant:
You do, with corners at (0,1),(0,4),(1,0),(3,0) and the intersection
of the blue and the green line, which you can determine.
===========================================
Cheers,
Stan H.
|
|
|
