Maliki manages a service center in the City of Sudluvy. The center opens at $7$:$00$ am everyday

and closes at $7$:$00$ pm$.$ Each day, Maliki has several employees on call; the exact number

depends on each day$$s needs. To better manage the operations of the center, Maliki divides the

daily $12-$hour work period into $24-$half$-$hour periods.

You have been hired by Maliki to build an optimal schedule for next week to minimize the total

number of employees on call each day. Since Maliki has forecasted the same number of required

employees for each day of the week, you can build the schedule for only one day. Table $1$ below

shows the forecasted number of required employees for each half$-$hour period.

Maliki$$s center has $10$ different shifts per day. The start time and duration of each shift is shown

in Table $2.$