Question 1202382
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.


<img src = "http://theo.x10hosting.com/2023/052102.jpg">


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 <a href = "https://www.desmos.com/calculator" target = "_blank">https://www.desmos.com/calculator</a>


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.