your friend is trying to find the maximum value of p=-x+3y subject to the following four constraints
{y<= -2x+6
y<= x+3
x>=0
y>=0
a.explain what error your friend made in the graph below
b.list the vertices of the feasible region
c.show all calculations to prove how to maximize the object function P
(a) no graph
(b) just find where the lines intersect. Clearly, on the axes, we have (0,0), (0,6), (0,3), (3,0), (-3,0)
Now find where the two sloping lines intersect.
(c) now evaluate p at the vertices.
p(0,0) = 0
and so on