Here is the optimal tableau for a standard Max problem.

$\left[\begin{array}{ccccccccc}z& x_1& x_2& x_3& x_4& s_1& s_2& s_3& rhs\\ 1& 0& 5& 3& 0& 6& 5& 0& 2700\\ 0& 1& \mathrm{.}3& 7\mathrm{.}5& 0& -\mathrm{.}1& \mathrm{.}2& 0& 6\\ 0& 0& 28& 360& 0& -8& 12& 1& 60\\ 0& 0& -\frac{1}{15}& -3& 1& \frac{1}{15}& -\frac{1}{10}& 0& 2\end{array}\right]$

$($a$).$The original rhs was $\left[\begin{array}{c}300\\ 180\\ 300\end{array}\right]$ but if the value of $b_1$ is changed to $307$ then new optimal value of tilde$(z)$ is

$($b$).$Using B$-$matrix type methods to update the given tableau followed, if needed, by simplex algorithm, we answer:

$(1).$Alternatively $($no change to $b_1),$ if the value of $c_3$ is increased by $5,$ then the new optimal value of tilde$(z)$ will be

$(2).$Finally, if the original value of $c_1$ is decreased by $20($too much!$),$ what is the new optimal value of tilde$(z)$