Determine an optimal schedule of start time and number of volunteers.

A public hospital employs volunteers to attend the reception between 8:00 A.M. and 10:00 P.M. Each volunteer works three consecutive hours, except those who enter at 8:00 P.M., who only work 2 hours. An approximation to the minimum need for volunteers is through a staggered function in two-hour intervals, which start at 8:00 A.M. and they are 4, 6, 8, 6, 4, 6 and 8 volunteers per interval. As most of the volunteers are pensioners, they are willing to offer their services at any time of the day (8:00 A.M. to 10:00 P.M.). However, as most charities compete for your services, the amount required should be kept as low as possible. Determine an optimal schedule of start time and number of volunteers.

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