A manager intends to order a new machine and must now decide on the number of spare parts to order along with the machine. The parts cost $$438$ each and have no salvage value. The manager has compiled the frequency distribution for the probable usage of spare parts: $6$ spare parts with frequency $0\mathrm{.}21$;$7$ spare parts with frequency $0\mathrm{.}1$;$8$ spare parts with frequency $0\mathrm{.}05$;$9$ spare parts with frequency $0\mathrm{.}11$ ; and $10$ spare parts with frequency $0\mathrm{.}53.$ For what range of shortage costs would stocking $8$ spare parts constitute an optimal decision?

a$.$ Between $196\mathrm{.}8$and $246\mathrm{.}4$

b$.$ Between $295\mathrm{.}2$and $369\mathrm{.}6$

c$.$ Between $98\mathrm{.}39$ and $123\mathrm{.}2$

d$.$ Between $236\mathrm{.}1$ and $295\mathrm{.}7$