Exercises 4.2

Finding Basic Feasible Solutions

If you want a basic feasible solution to remain feasible after pivoting, then you must choose a leaving variable that has the smallest positive quotient.

The tableau below represents a standard maximizing problem. Suppose it is required that x4 enter. We want to choose a leaving variable.

Basic x1 x2 x3 x4 x5 RHS Quotient Leaving
x -10
x undefined
x 10
Entering

Exercises (assume that x4 enters)

  1. What is the current basic solution?
  2. What happens if you choose x5 to leave?
    Why?
  3. Choose x1 to leave then pivot. What happens to the basic feasible solution?
    Why?
  4. Make x2 leave. What is the corresponding basic solution?

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