Question 1202382: Graph the following system of linear inequalities.
{y≥0x≥02x+2y≥22x≥y
What are the corner points of the system?
Next, find a point that is in the feasible set of the system, but not on any of the boundary lines:
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! using the desmos.com calculator, you would graph the opposite of the inequalities.
the area of the graph that is not shaded is your region of feasibility.
your inequalities are:
{y≥0x≥02x+2y≥22x≥y
y >= 0
x >= 0
2x + 2y >= 22
x >= y
you would graph:
y <= 0
x <= 0
2x + 2y <= 22
x <= y
here's what the graph looks like.
the corner points of your feasibility region are:
(5.5,5.5)
(11,0)
a point in the feasibility that is not at a corner point would be (15,5).
all the inequalities must be true at each of the corner points and anywhere in the feasible region.
at (5.5,5.5):
y >= 0 is true
x >= 0 is true
2x + 2y >= 22 = 11 + 11 >= 22 which is true.
x >= y is true
at (11,0):
y >= 0 is true
x >= 0 is true
2x + 2y >= 22 = 22 + 0 >= 22 which is true.
x >= y is true
at (15,5):
y >= 0 is true
x >= 0 is true
2x + 2y >= 22 = 30 + 10 >= 22 which is true.
x >= y
desmos.com calculator can be found at https://www.desmos.com/calculator
note that you have an open ended feasible region.
the corner points of this region would most likely contain the minimum value of the objective function, if you had one.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
To write math expression correctly, use dividers to separate them.
It is the same rule as to use dividers between words and sentences,
when you write a text. Clear ? Are you familiar with it ?
In your post, math expressions are written
as if you write them in the first time in your life . . .
It is even better to write each separate math expression
in separate line to avoid mess.
Do not try to make your writing as bad as possible to perplex the readers.
Your goal is not to perplex the readers.
Make it in OPPOSITE way: do it as good as you can.
It will make much more sense - FOR YOU.
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