# Question

Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve the following MIP problem interactively:

Minimize Z = 5x1 + x2 + x3 + 2x4 + 3x5,

Subject to

and

xj ≥ 0, for j = 1, 2, 3, 4, 5

xj is integer, for j = 1, 2, 3.

Minimize Z = 5x1 + x2 + x3 + 2x4 + 3x5,

Subject to

and

xj ≥ 0, for j = 1, 2, 3, 4, 5

xj is integer, for j = 1, 2, 3.

## Answer to relevant Questions

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 In Sec. 12.8, at the end of the subsection on tightening constraints, we indicated that the constraint 4x1 – 3x2 + x3 + 2x4 ≤ 5 can be tightened to 2x1 – 3x2 + x3 + 2x4 ≤ 3 and then to 2x1 – 2x2 + x3 + 2x4 ≤ 3. ...Generate as many cutting planes as possible from the following constraint for a pure BIP problem. 5x1 + 3x2 + 7x3 + 4x4 + 6x5 ≤ 9. Consider the problem of determining the best plan for how many days to study for each of four final examinations that is presented in Prob. 11.3-3. Formulate a compact constraint programming model for this problem. Suppose that a mathematical model fits linear programming except for the restriction that |x1 – x2 | = 0, or 3, or 6. Show how to reformulate this restriction to fit an MIP model.Post your question

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