# Question

Consider the following nonlinear BIP problem:

Maximize

Subject to

xj is binary, for j = 1, 2, 3, 4.

Maximize

Subject to

xj is binary, for j = 1, 2, 3, 4.

## Answer to relevant Questions

Consider the Lagrangian relaxation described near the end of Sec. 12.6. Reconsider the IP model of Prob. 12.5-2. (a) Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve this problem by hand. For each subproblem, solve its LP relaxation graphically. (b) Now use the interactive ...For each of the following constraints of pure BIP problems, use the constraint to fix as many variables as possible: (a) 4x1 + x2 + 3x3 + 2x4 ≤ 2 (b) 4x1 – x2 + 3x3 + 2x4 ≤ 2 (c) 4x1 – x2 + 3x3 + 2x4 ≥ 7 Apply the procedure for tightening constraints to each of the following constraints for a pure BIP problem: (a) x1 + 3x2 – 4x3 ≤ 2. (b) 3x1 – x2 + 4x3 ≥ 1. Consider the following problem: Maximize Subject to x1 ∈ {25, 30}, x2 ∈ {20, 25, 30, 35, 40, 50}, x3 ∈ {20, 25, 30}, x4 ∈ {20, 25}, all these variables must have different values, x2 + x3 + 60, x1 + x3 + 50.Post your question

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