Linear Programming Assignment 1
AMP15W2
a) Degeneracy in the Simplex Method
Given the following linear programming problem:
Maximize Z = 2x1 + 3x2
Subject to:
x1 + 3x2 ≤ 6,
2x1 + 5x2 ≤ 10,
4x1 + 2x2 = 8,
x1 , x2 ≥ 0
• Convert this problem into standard form. Discuss the challenges arising
from the equality constraint and how you address them using the Simplex
method.
b) Cycling in Simplex Method
Solve the problem using the Simplex method. Demonstrate how cycling can
occur during the solution process. Then, show how the Bland’s Rule can be
applied to prevent cycling.
c) Non-Optimal Initial Basic Feasible Solution
Assume a different initial basic feasible solution (BFS) that is not optimal. Use
the Simplex method to iterate through the solution process, and show the steps
needed to move toward the optimal solution from the non-optimal BFS.
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