A hospital administrator has the following minimal daily requirements for nursing

personnel:

Clock time Minimal Number

Period $(24-$Hour Day$)$ of Nurses Required

$1$

$2$

$3$

$4$

$5$

$6$

$6$AM$-10$AM

$10$AM$-2$PM

$2$PM$-6$PM

$6$PM$-10$PM

$10$PM$-2$AM

$2$AM$-6$AM

$60$

$70$

$60$

$50$

$20$

$30$

Nurses report to the hospital wards at the beginning of each period and work for $8$ consec

utive hours. The hospital wants to determine the minimal number of nurses to employ so that

there will be sufficient number of nursing personnel available for each period. Formulate this

as a linear programming proble