A certain restaurant operates $7$ days a week. Waiters are hired to work $6$ hours per day. The union contract specifies that each waiter must work $5$ consecutive days and then have $2$ consecutive days off. All waiters receive the same weekly salary. Staffing requirements are shown in the following table.

Day Required number of waiter hours

Monday $150$

Tuesday $200$

Wednesday $400$

Thursday $300$

Friday $700$

Saturday $800$

Sunday $300$

The manager wishes to find an employment schedule that satisfies these requirements at minimum cost. Formulate an appropriate mathematical model.