$[8$ marks$]$ Recall the Par, Inc., problem. Find the ranges of optimality if the profit contribution for the standard bag is $$100$ and deluxe bag is $$9.($You must show your work$).$

Max $100S+9D$

$s.t.$

$\frac{7}{10}S+1D630$

$\frac{1}{2}S+\frac{5}{6}D600$

$1S+\frac{2}{3}D708$

$\frac{1}{10}S+\frac{1}{4}D135$

$S,D0$