Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / T / 2 / b / i

For this tableau sign convention, a negative coefficient in the objective row means the corresponding nonbasic variable can increase profit. Initially $x_3$ has the most negative coefficient. The simplex ratio test gives $33/5$ in row one and $18/3=6$ in row two, so row two leaves to preserve feasibility. Next $x_1$ is the only column with a negative objective coefficient. The ratios are $3/(1/3)=9$ and $6/(1/3)=18$, so row one leaves. All resulting basic variables remain nonnegative.