# Question

Consider the following statements about any pure IP problem (in maximization form) and its LP relaxation. Label each of the statements as True or False, and then justify your answer:

(a) The feasible region for the LP relaxation is a subset of the feasible region for the IP problem.

(a) The feasible region for the LP relaxation is a subset of the feasible region for the IP problem.

## Answer to relevant Questions

Consider the assignment problem with the following cost table: (a) Design a branch-and-bound algorithm for solving such assignment problems by specifying how the branching, bounding, and fathoming steps would be performed. ...Consider the following IP problem: Maximize Z = –3x1 + 5x2, Subject to 5x1 – 7x2 ≥ 3 and xj ≤ 3 xj ≥ 0 xj is integer, for j = 1, 2. (a) Solve this problem graphically. (b) Use the MIP branch-and-bound algorithm ...Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve the following MIP problem interactively: Maximize Z = 5x1 + 4x2 + 4x3 + 2x4, Subject to and xj ≥ 0, for j = 1, 2, 3, 4 xj is integer for j = 1, 2, 3. 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. ...Consider the following BIP problem: Maximize Subject to and all xj binary.Post your question

0