a$)$ Solve the following Primal Lincor programming using the Big$-$M Method.

Min $2=\frac{3}{x}$I $+2x2$

$S.T.\frac{?}{xI}+2240$

$2x1+x_2=50$

$x1,x20$

b$)$ If we decrease the cost of X $2$ to $1,$ would the solution stay optimum? Why?

c$)$ What is the maximum change in resource I that keeps the solution optimum?

d$)$ Write the dual problem for the primal problem in part a$.$

e$)$ What is the solution to the dual LP of part $b?($find the solution from the optimum of the Primal problem solution in part a$)$

f$)$ What does adding the following dual constraint mean?

$y1+y25$