Linear Algebra and Its Applications · Problem 8.2.1

Linear Programming and Game Theory — Gilbert Strang

Mathematics · simplex-method-entering-leaving-variables

Problem

Minimize

x_1 + x_2 - x_3

, subject to

\begin{aligned} 2x_1 - 4x_2 + x_3 + x_4 &= 4\\ 3x_1 + 5x_2 + x_3 \phantom{{}+x_4} + x_5 &= 2. \end{aligned}

Which of

x_1, x_2, x_3

should enter the basis, and which of

x_4, x_5

should leave? Compute the new pair of basic variables, and find the cost at the new corner.