Problem $1($Employee Schedule Optimization$)$

The manager of the Air$-$Express hub operates seven days a week, and the number of packages it handles each day varies from one day to the next. Using historical data on the average number of packages received each day, the manager estimates the number of workers needed to handle the packages as:

Day of Week

Workers Required

Sunday

$21$

Monday

$27$

Tuesday

$18$

Wednesday

$29$

Thursday

$19$

Friday

$25$

Saturday

$19$

$$

Each worker works on $3$ consecutive days, with $4$ consecutive days off as follows:

Shift

Days Off

Wage

$1$

Sun, Mon, Tues, Wed

$$600$

$2$

Mon, Tues, Wed, Thurs

$$710$

$3$

Tues, Wed, Thurs, Fri

$$735$

$4$

Wed, Thurs, Fri, Sat

$$725$

$5$

Thurs, Fri, Sat, Sun

$$680$

$6$

Fri, Sat, Sun, Mon

$$690$

$7$

Sat, Sun, Mon, Tues

$$650$

The manager wants to keep the total wage expense for the hub as low as possible. With this in mind, how many package handlers should be assigned to each shift if the manager wants to have a sufficient number of workers available each day?