# Question

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 presented in Sec. 12.7 to solve this problem by hand. For each subproblem, solve its LP relaxation graphically.

(c) Use the binary representation for integer variables to reformulate this problem as a BIP problem.

(d) Use the BIP branch-and-bound algorithm presented in Sec. 12.6 to solve the problem as formulated in part (c) interactively.

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 presented in Sec. 12.7 to solve this problem by hand. For each subproblem, solve its LP relaxation graphically.

(c) Use the binary representation for integer variables to reformulate this problem as a BIP problem.

(d) Use the BIP branch-and-bound algorithm presented in Sec. 12.6 to solve the problem as formulated in part (c) interactively.

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