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<math>\boldsymbol{x_B}</math> must be correspondingly decreased by <math>\Delta \boldsymbol{x_B} = \boldsymbol{B}^{-1} \boldsymbol{A}_q x_q</math> subject to <math>\boldsymbol{x_B} - \Delta \boldsymbol{x_B} \ge \boldsymbol{0}</math>. Let <math>\boldsymbol{d} = \boldsymbol{B}^{-1} \boldsymbol{A}_q</math>. If <math>\boldsymbol{d} \le \boldsymbol{0}</math>, no matter how much <math>x_q</math> is increased, <math>\boldsymbol{x_B} - \Delta \boldsymbol{x_B}</math> will stay nonnegative. Hence, <math>\boldsymbol{c}^{\mathrm{T}} \boldsymbol{x}</math> can be arbitrarily decreased, and thus the problem is unbounded. Otherwise, select an index <math>p = \operatorname{argmin}_{1 \le i \le m} \{x_i / d_i \mathop{|} d_i > 0\}</math> as the ''leaving index''. This choice effectively increases <math>x_q</math> from zero until <math>x_p</math> is reduced to zero while maintaining feasibility. The pivot operation concludes with replacing <math>\boldsymbol{A}_p</math> with <math>\boldsymbol{A}_q</math> in the basis.
==Numerical example==
==Practical issues==
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