# Help to learn this LPP sample

I'm with many difficulties to understand a LPP.

This is the problem:

This is the Tableau:

After the first iteration:

After the second iteration:

Until here I understand everything, but...

This is the solution:

I can't understand the numbers of the solution.

The Pivot Value from second iteration, before the solution is -5? It is the less number, why the 5/3 it is the Pivot Number instead -5?

To find pivot row (after you determine pivot column), one must consider the ratios of constants by pivot column elements and select the smallest ratio. Consider the pivot column $x_5$: $$\frac{8}{\frac{5}{3}}=4.8 \ (1) \\ \frac{0.5}{\frac53}=0.3 \ (2) \\ \frac{3}{-5}=-0.6 \ (3)$$ However, if the ratio is negative, it is ignored. So, $(3)$ is ignored and $(2)$ is the smallest ratio.