# Question

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,

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,

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