A store is having a 12-hour sale. The total number of shoppers who have entered the store thours after it begins is modeled by the function S defined by $S(t)=0.5 t^4-16 t^3+144 t^2$ for $0 \leq t \leq 12$. At time $t=0$, when the sale begins, there are no shoppers in the store. The rate at which shopper's leave the store, measured in shoppers per hour, is modeled by the function $L$ defined by $L(t)=-80+\frac{4400}{t^2-14 t+55}$ for $0 \leq t \leq 12$. According to the model, how many shoppers are in the store at the end of the sale (time $t=12$ )? Give your answer to the nearest whole number.
