Suppose that for a given optimization problem: at least one of the following two constraints needs to be satisfied by the optimal solution:

3x₁ + 2x₂ 18 x₁ + 4x₂ 16

That is, we need to allow for the possibility that the optimal solution may not satisfy one of the constraints if the other constraint is satisfied. To code this requirement into the optimization problem, we redefine the first constraint using a binary variable y:

3x₁ + 2x₂ 18 + My,

where x₁, x₂ cannot exceed a large (enough) positive number M.

How should the second constraint be redefined?

x₁ + 4x₂ 16 + M

x₁ + 4x₂ 16y

x₁ + 4x₂ 16 + M(1 - y)

x₁ + 4x₂ 16(1 - y)

x1 + 4x2 16 + M(y)