Princeton Algorithms: Part 2 [week 7: Linear Programming]

Exercise

Question Explanation

The basis is { x7, x1, x5 }.
The nonbasic variables are { x0, x2, x3, x4, x6 }.
The entering variables are those nonbasic variables with a positive objective function coefficient.

Question Explanation

The basis is { x1, x2, x3, x4, x7 }.
The nonbasic variables are { x0, x5, x6, x8 }.
The entering variable is x6.
The min ratio test determines the leaving variable: min ratio = { *, 8/3, 8/3, 60, 3 } = 8/3.
The minimum occurs in rows 1 and 2, which corresponds to basic variables x2 and x3.
The leaving variables are { x2 x3 }.

Interview Question