Consider the following integer nonlinear programming problem:
Maximize Z = 4x21 €“ x31 + 10x22 €“ x42,
Subject to
x1 + x2 ‰¤ 3
and
x1 ‰¥ 0, x2 ‰¥ 0
x1 and x2 are integers.
This problem can be reformulated in two different ways as an equivalent pure BIP problem (with a linear objective function) with six binary variables (y1 j and y2 j for j = 1, 2, 3), depending on the interpretation given the binary variables.
(a) Formulate a BIP model for this problem where the binary variables have the interpretation,

If Xi = J yj 0 otherwise