Question $2(50$ points$)$ You are hired by another company that is also looking to maximize Its proit

rom two different products they make. Considering the information below and using the Fundamental

nsight, please answer the questions.

$c=\left[\begin{array}{cc}2& 3\end{array}\right],b=\left[\begin{array}{c}42\end{array}\right]$

$36$

$30,A=\left[\begin{array}{cccc}1& 2& 1& 1\end{array}\right]$

$1$

$2$

$x_B^{**}=\left[\begin{array}{ccc}{x}_2& x_1& x_5\end{array}\right],S^{**}=B_2^{-1}=\left[\begin{array}{ccccccc}0\mathrm{.}667& -0\mathrm{.}333& 0& 0\mathrm{.}667& 0& -0\mathrm{.}333& 1\end{array}\right]$

$-0\mathrm{.}333$

$-0\mathrm{.}333$

a$)$ What are the optimal values of the decision variables $($production level of two products$)?$

b$)$ What is the objective function value at the optimal solution $($maximum profit$)?$

c$)$ Please provide the complete final tableau $($optimal$).$

d$)$ How would the objective function change if the availability of the third constraint increased from

$30$ to $35?$