I am trying to solve the following system of inequalities in Mathematica but the output is just the same system of inequalities. I need to get the expressions for x, y in terms of the pi indexed constants.
I tried renaming the pi constants {a,b,c,d} but still no significant output.
I would truly appreciate your help, PM
FindInstance[{x >= a, x + y >= b, x + 2 y >= c, y >= a, 2 y >= b, 2 x + 2 y == d, c == a + b, b >= 2 a, d >= 2 b}, {x, y}]
Or equivalently
FindInstance[{x >= Subscript[pi, 1], x + y >= Subscript[pi, 2], x + 2 y >= Subscript[pi, 3], y >= Subscript[pi, 1], 2 y >= Subscript[pi, 2], 2 x + 2 y == Subscript[pi, 4], Subscript[pi, 3] == Subscript[pi, 1] + Subscript[pi, 2], Subscript[pi, 2] >= 2 Subscript[pi, 1], Subscript[pi, 4] >= 2 Subscript[pi, 2]}, {x, y}, reals]