Why is this not a quantified system of equations and inequalities?

Questions
,
1

I’m attempting to Reduce four equations with respect to four unknown variables as follows:

Reduce[{
   w == Max[(72 - x - 3 y)/4, 0],
   x == Max[(60 - w - z)/2, 0],
   y == Max[(48 - z - 2 w)/3, 0],
   z == Max[(60 - y - x)/2, 0]}
  {w, x, y, z}
 ]

When I evaluate, Mathematica tells me this system is not a quantified system of equations and inequalities. Can anybody help explain why?

2

You are missing a comma: :wink:

In[4]:= Reduce[{w == Max[(72 - x - 3 y)/4, 0], 
  x == Max[(60 - w - z)/2, 0], y == Max[(48 - z - 2 w)/3, 0], 
  z == Max[(60 - y - x)/2, 0]}, {w, x, y, z}]

Out[4]= w == 78/5 && x == 48/5 && y == 0 && z == 126/5