# Linear Programming - Cyclic Algorithm (The Cutting Plane)

Please see the attachment for full details of the question.

(a) Use the Cyclic (i.e. the cutting plane) algorithm to solve the attached integer linear programming problem.

(b) Draw a graph to illustrate your solution form (a). Show all cuts generated and the solution obtained at each iteration.

(c) Explain how the Cyclic algorithm would handle any artificial variables that were basic at the end of phase 2.

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#### Solution Preview

a. Use the cyclic algorithm to solve the following integer linear programming problem:

Maximize: z=3x1 + x2

Subject to: 3x1 + x2 < 10

X1 + 2x2 < 9

X1, x2 > 0

Z, x1 and x2 integer

Step 1: We determine the intersection of the constraints.

Current solution (Sol_): X1 = 2.2 and X2 = 3.4 which is not optimal as both values are not integers.

Step ...

#### Solution Summary

The solution deals with estimating the solution of a set of constraints and objective function.