Order On The Tape

Three files are written end to end on a tape. To read a file the drive must scan past everything stored before it, so if file $k$ sits at position $k$ the cost of one read is the total length of files 1 through $k$. Each file will be read a known number of times over the life of the tape, so the total cost of an ordering $\pi$ is

$\Sigma\text{cost}(\pi) = \sum_{k=1}^{n} F[\pi(k)] \cdot \sum_{i=1}^{k} L[\pi(i)]$

Which ordering minimises the total, and what does it cost?