Chapter 4.7, Problem 9P

Explanation of Solution

Linear program

• Clearly any bfs having x₅=0 is optimal.
• Trying all combinations of basic variables not involving x₅ yields the three following alternative optimal bfs which include

  $\left[\begin{array}{c}2\\ 5\\ 0\\ 0\\ 0\end{array}\right]$ $\left[\begin{array}{c}0\\ 1\\ 2\\ 0\\ 0\end{array}\right]$ $\left[\begin{array}{c}0\\ 7/3\\ 0\\ 2/3\\ 0\end{array}\right]$

• Thus the set of all optimal solutions may be written in the form

    a $\left[\begin{array}{c}2\\ 5\\ 0\\ 0\\ 0\end{array}\right]$