Jim$-$O$\text{'}$s fast focus restaurant is opening up a new branch. Based on demand forecast the following service personnel levels are anticipated. This week's schedule must satisfy the following two requirements: $(1)$ each of the employees must have two consecutive days off; $(2)$ at least two employees must be allowed to be off on the weekend $($Saturday and Sunday$).($Since Monday is used as the first day of the pay week, an employee cannot be off on both Sunday and Monday.$)$ What is the minimum number of employees that needs to be hired? $($Hint: Appropriately extend the Excel Linear Programming model discussed in class to find the answer.$)$

Days of Week

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

Staff needs

$5$

$4$

$3$

$4$

$6$

$6$

$5$

$$

A$.$

$10$

B$.$

$6$

C$.$

$8$

D$.$

$7$

E$.$

$12$