A firms$$ inventory records indicated the following transactions for the year. January $1$ Beginning Balance $200$ units @ $ $100/$unit; February $14$ Purchased $1,400$ units @ $ $101/$unit; June $21$ Purchase $1,300$ units @ $ $104/$unit; December $4$ Purchased $1,100$ units @ $ $102/$unit; Sales total $3,750$ units at $ $200$ each. What amount should be reported for cost of goods sold if the firm applies LIFO $($periodic$)?$

a$.$ $ $383,300.$

b$.$ $ $383,750.$

c$.$ $ $750,000.$

d$.$ $ $383,250.$

e$.$ Cannot be determined.