A tank initially contains $125$ kg of water $.$ At this time $,$a feed stream enters the tank with a mass flow rate of mi$=0\mathrm{.}5$ e$^-0\mathrm{.}10$t$,$ where mi is in kg$/$min and t is time in minutes. At the same time, an outlet stream with mo$=0\mathrm{.}4$ kg$/$ min exits the tank. Determine the maximum mass of water in the tank,in kg$.$

a$)112\mathrm{.}50$

b$)125$

c$)206\mathrm{.}20$

d$)75\mathrm{.}95$

e$)126\mathrm{.}50$