A school is preparing a trip for $400$ students. The company who is providing the transportation has $10$ large buses of $50$ seats each and $8$ small buses of $40$ seats, but only has $9$ drivers available. The rental cost for a large bus is $$800$ and $$600$ for the small bus. Formulate the problem to minimize the rental costs for the school in terms of the following decision variables:

S: number of small buses to rent

L: number of large buses to rent

A$.$

min $600$S $+800$L subject to: $40$S $+50$L $>=9$; S $<=8$; L $<=10$; S $+$ L $<=400$; S$,$ L $>=0$; S$,$ L are integers

B$.$

min $600$S $+800$L subject to: $40$S $+50$L $>=400$; S $<=8$;$$ L $<=10$; S $+$ L $<=9$; S$,$ L $>=0$

C$.$

min $600$S $+800$L subject to: $40$S $+50$L $>=400$; S $<=8$; L $<=10$; S $+$ L $<=9$; S$,$ L $>=0$; S$,$ L are integers

D$.$

min $600$S $+800$L subject to: $50$S $+40$L $>=400$; S $<=8$; L $<=10$; S $+$ L $<=9$; S$,$ L $>=0$