 Solution

Introduce nonnegative slack variables $s_1,s_2$ and let $z$ denote profit. We display each simplex tableau as coefficients of its row equation, with the coefficient of $z$ in the objective equation implicitly one. Thus a negative coefficient in the last row permits an improving entering variable. The initial simplex tableau isUse the simplex method with $x_2$ entering. The simplex ratio test gives ratios $6/2=3$ and $6/1=6$, so $s_1$ leaves. Divide its row by two and eliminate the other $x_2$ entries:Next $x_1$ enters. The positive-column ratios are $3/(1/2)=6$ and $3/(3/2)=2$, so $s_2$ leaves. After this pivot and a row reordering,The last row is $z=14-(5/3)s_1-(2/3)s_2$, so every nonnegative feasible solution has $z\le 14$. Setting the nonbasic variables to zero givesThe equality certificate also shows uniqueness, since both nonbasic objective coefficients are strictly unfavorable.