A Hospital Needs to Determine How Many Nurses to Hire

Essay

A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4-hour time period and their wages are shown in the following table.
$\begin{array}{lcc}\text { Time period } & \text { Required \# of Nurses } & \text { Wage }(\$ / \mathrm{hr}) \\\hline 12 \mathrm{am}-4 \mathrm{am} & 20 & 15 \\\quad 4 \mathrm{am}-48 & 30 & 16 \\\text { am } & & \\\quad 8 \mathrm{am}-12 \mathrm{pm} & 40 & 13 \\12 \mathrm{pm}-4 \mathrm{pm} & 50 & 13 \\4 \mathrm{pm}-4 & 40 & 14 \\\\\mathrm{pm} \\8 \mathrm{pm}-12 \mathrm{am} &30 & 15\end{array}$
Formulate the LP for this problem.