Question

How do you graph this u(x,y)=x+min(x,y)

Answer 1

i think what your want to ask is to draw the indifference curve.
we might assume x>0, y>0. first draw the line x = y, the points in area A1 which is surrounded by x-axis and x = y have the property x>y.
the points in area A2 which is surrounded by y-axis and x = y have the property y>x.
then let's draw 10=x+min(x,y), u =10, assume x>y, get x+y=10, draw x+y=10 in the area A1, then assume x<y, get x = 5, draw x=5 in the area A2. done.