Each month, a vacuum cleaner manufacturing cell had $800$ hours of time available.$$ During that time, the cell could have manufactured up to $2,400$ vacuum cleaners, but only $1,600$ vacuum cleaners were actually manufactured. $$ Required: Calculate the following $($show your work$)$: a$.$ Theoretical cycle time in minutes b$.$ Theoretical velocity per hour c$.$ Actual cycle time in minutes d$.$ Actual velocity per hour