You$$re scheduling shifts at a customer call center for a period of n hours. Each shift is defined

by a start time and duration. Shifts start at the top of the hour and should be scheduled in discrete hourly

intervals. Workers$$ preferences and labor laws dictate a few additional conditions:

$($i$)$ each shift must be at least L and at most U hours long;

$($ii$)$ workers are paid at an hourly rate of r dollars $/$ hour, and must be hired for full shifts; that is$,$ if a worker

is assigned to any part of a shift, you must pay them for the whole shift.

Given estimates of the volume of calls over time, you know that there must be a minimum number of workers

on duty m$\_$i for each service hour i in $[$n$].$ Design an algorithm to partition the n hours into shifts, and decide

how many workers should be on duty, in a way that minimizes the total cost in wages to the call center, subject

to the workers$$ preferences and minimum staffing constraints.