NO - Summary of Chapter 3 (Part VI)

Knowing that the objective function of the basis/non-basis formulation of an LP is:

$$\min c_B^t{B}^{-1}\left(b-N{x}_N\right)+c_N{x}_N$$

we can define a reduced cost:

$$c_N^t-c_B^t{B}^{-1}N$$

Which is the part of the objective function that changes when increasing $x_N$. Then we can say that if the reduced cost is $<0$ than there exist a descent direction of $x_N$ such that we can find a better solution. Because, multiplying the reduced cost, which we have said is $<0$ , with $x_N$, which is $\ge 0$ (because of the constraint), then the objective function will decrease, so we have found a better solution.