Mazy$$s Department Store has decided to stay open a $24-$hours basis. The store manager has divided the $24-$hour day into six $4-$hour periods and determined the following minimum personnel requirements for each period.

Time

Personnel Needed

Midnight$-4$:$00$ A$.$M$.$

$90$

$4$:$00$A$.$M $8$:$00$ A$.$M

$215$

$8$:$00$A$.$M$-$Noon

$250$

Noon$-4$:$00$ P$.$M$.$

$65$

$4$:$00$ P$.$M $-8$:$00$ P$.$M$.$

$300$

$8$:$00$ P$.$M $-$Midnight

$125$

Personnel must report for the work at the beginning of one of the above times and work $8$ consecutive hours. The store manager wants to know the minimum number of employees to assign each $4-$hours segment to minimize the total number of employees. Formulate a linear programming model for this problem.