Could you explain this solution more in detail why leading coefficients of constraints cannot be negative to become an entering variable?

References: optimization, simplex method, reduced costs, linear program, basic solution, standard equality form

1. Find an example of a tableau for a linear program in standard equality form, such that at least one of the reduced costs is strictly positive, and yet the corresponding basic solution is optimal. The following tableau is a linear program that is in standard equality form. 2 23161 +34 = 4 1x1 x2 :r:4 = 2 2:91 + :33 :c4 = 2 This tableau is optimal with 4 23) a'=(0220) HUUN II We see that while the reduced cost of :32 is (2), which is strictly positive, the tableau is optimal because there is not a choice for an entering variable since both of the leading coeicients of the contraints are negative. Also, 9:4 is not a candidate to enter the basis because the reduced cost is strictly negative. Therefore, we have a tableau with at least one of the reduced costs strictly positive while the corresponding solution is optimal