The Gotham City Police Department employs $30$ police officers. Each officer works $5$ days per week. The crime rate fluctuates with the day of the week, so the number of police officers required each day depends on which day of the week it is: Saturday, $28$; Sunday, $18$; Monday, $18$; Tuesday, $24$; Wednesday, $25$; Thursday, $16$; Friday, $21.$ The police department wants to schedule police officers to minimize the number whose days off are not consecutive. Formulate an LP that will accomplish this goal. $($Hint: Have a constraint for each day of the week that ensures that the proper number of officers are not working on the given day.$)$