Questions $1-6$

Use the following problem statement to answer questions $1-6.$

A hospital wants to determine the nursing schedule to minimize total cost. Their staff consist of

full$-$time nurses who work eight$-$hour shifts and part$-$time nurses who work four$-$hour shifts.

The supervisor of nurses divides the day into six four$-$hour periods. In each period, a different

level of demand requires different numbers of nurses to hire. The minimum number of nurses

required is shown in Table $1.$ It is also required that there must be at least $5$ full$-$time nurses at

each time period. The full$-$time nurses get paid $$100$ per shift while the part$-$time nurses get

paid $$40$ per shift. The normal shifts can begin at the start of any of the four$-$hour periods.

$[$Note: $=$ no$.$ of full$-$time nurses beginning their shift at time period i $,$ where $i=1,2,3,4,5,$ and

$Yi=$ no$.$ of part$-$time nurses beginning their shift at time period i $,$ where $i=1,2,3,4,5,$ and $6.]$

Time Period

Min. number of nurses needed

$44$ points

Which of the following constraints is correct?

$x1+x45$

$x1+x25$

$4$ points

Which of the following constraints is correct?

$x1+x5+Y1<mn\; id="EditorElement\_2484067">2</mn><mn\; id="EditorElement\_2484068">0</mn>$

$x1+x6+Y120$

$6$

$4$ points

Which of the following constraints is correct?

$x2+x6+Y6<mn\; id="EditorElement\_2483935">1</mn><mn\; id="EditorElement\_2483936">7</mn>$

$x2+x3+Y317$