In the THE multiprogramming system [DIJK68], a drum (precursor to the disk for secondary storage) is divided into input buffers, processing areas, and output buffers, with floating boundaries, depending on the speed of the processes involved. The current state of the drum can be characterized by the following parameters:

max = maximum number of pages on drum

i = number of input pages on drum

p = number of processing pages on drum

o = number of output pages on drum

reso = minimum number of pages reserved for output

resp = minimum number of pages reserved for processing

Formulate the necessary resource constraints that guarantee that the drum capacity is not exceeded and that a minimum number of pages is reserved permanently for output and processing.