# Question: Consider the following IP problem Maximize Z 3x1 5x2 Subject

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.

## Answer to relevant Questions

The board of directors of General Wheels Co. is considering six large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will ...A machine shop makes two products. Each unit of the first product requires 3 hours on machine 1 and 2 hours on machine 2. Each unit of the second product requires 2 hours on machine 1 and 3 hours on machine 2. Machine 1 is ...Use the following set of constraints for the same pure BIP problem to fix as many variables as possible. Also identify the constraints which become redundant because of the fixed variables. Generate as many cutting planes as possible from the following constraint for a pure BIP problem: 3x1 + 5x2 + 4x3 + 8x4 ≤ 10. 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.Post your question