SOLUTION: Given the system of inequalities below, determine the shape of the feasible region and find the vertices of the feasible region. Give the shape as "triangle", "quadrilateral", or "

Question 1161311: Given the system of inequalities below, determine the shape of the feasible region and find the vertices of the feasible region. Give the shape as "triangle", "quadrilateral", or "unbounded". Report your vertices starting with the one which has the smallest x-value. If more than one vertex has the same, smallest x-value, start with the one that has the smallest y-value. Proceed clockwise from the first vertex. Leave any unnecessary answer spaces blank.
x+y≤2
3x+y≥3
x+3y≥3
x≥0
y≥0
The shape of the feasible region is (a)?_____

The first vertex is
The second vertex is
The third vertex is
The fourth vertex is

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the shape of the feasible region is a triangle.
using the desmos.com calculator, you would graph the opposite of the inequalities.
the are on the graph that is not shaded is the region of feasibility.
the shape is a triangle.
the vertices of the feasible region are:
(5,1.5)
(.75,.75)
(1.5,.5)
the inequalities are:
x+y<=2
3x+y>=3
x+3y>=3
x>=0
y>=0
you would graph:
x+y>=2
3x+y<=3
x+3y<=3
x<=0
y<=0
here's what the graph looks like.

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