The Par, Inc., Problem $($revisited$).$ Refer to the Par, Inc., problem described in Section $2\mathrm{.}1.$ Suppose that Par, Inc.$$s management encounters the situations described below. If Par, Inc., encounters each of these situations separately, what is the optimal solution and the total profit contribution for each situation described? $($MLO $2\mathrm{.}12\mathrm{.}3)$

a$.$ The accounting department revised its estimate of the profit contribution for the deluxe bag to $$18$ per bag.

b$.$ A new low$-$cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $$20$ per bag. $($Assume that the profit contribution of the deluxe bag is the original $$9$ value.$)$

c$.$ New sewing equipment is available that would increase the sewing operation capacity to $750$ hours. $($Assume that $10$A $+9$B is the appropriate objective function.$)$