It appears that you're working on a Simplex method problem, and you've already completed the first iteration. Based on the image, I can see that you performed the first iteration correctly, identifying that $x_1$ enters and $S_3$ leaves. The pivot element is 8 (in the row corresponding to $S_3$ and the column corresponding to $x_1$).

I'll guide you through the second iteration step-by-step.

Step-by-Step to Perform the Next Iteration:

1. Pivoting: Divide the entire pivot row (the one with $S_3$) by the pivot element, which is 8.

   • New $S_3$ row will be: $\left( \frac{8}{8}, \frac{3}{8}, \frac{0}{8}, \frac{0}{8}, \frac{1}{8} \right) = (1, 0.375, 0, 0, 0.125)$

2. Row operations: Perform row operations on the other rows to make the column corresponding to $x_1$ zero.

   • For row $S_1$: Subtract 4 times the new pivot row from the current $S_1$ row. The original $S_1$ row is $(4, 5, 1, 0, 0)$, so: $(4, 5, 1, 0, 0) - 4 \times (1, 0.375, 0, 0, 0.125) = (0, 3.5, 1, 0, -0.5)$

   • For row $S_2$: Subtract 3 times the new pivot row from the current $S_2$ row. The original $S_2$ row is $(3, 2, 0, 1, 0)$, so: $(3, 2, 0, 1, 0) - 3 \times (1, 0.375, 0, 0, 0.125) = (0, 0.875, 0, 1, -0.375)$

   • For the Z-row: Add 5 times the new pivot row to the current Z-row. The original Z-row is $(-5, -4, 0, 0, 0)$, so: $(-5, -4, 0, 0, 0) + 5 \times (1, 0.375, 0, 0, 0.125) = (0, -2.125, 0, 0, 0.625)$

The Second Iteration Table:

The new simplex tableau after the second iteration will look like this: