A hospital employs volunteers to staff reception desk

A hospital employs volunteers to staff reception desk between 8.00 A.M. and 10.00 P.M. Each volunteer works three consecutive hours expect for those starting at 8.00 P.M. who work for two hours only. The minimum need for volunteers is approximated by a step function over 2-hour intervals starting at 8.00 A.M as 4,6,8,6,4,6,8. Because most volunteers are retired individuals, they are willing to offer their services at any hour of the day ( 8.00 A.M. to 10.00 P.M. ). However, because of the large number of charities competing for their services, the number needed must be kept as low as possible. Determine an optimal schedule for the start time of the volunteers.