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.
$\begin{array}{lll}\text { Time period }&\text { Required \# of Nurses }&\text { Wage } \$ / h r)\\\hline12 \mathrm{am}-4 \mathrm{am} & 20 & 15 \\4 \mathrm{am}-8 \mathrm{am} & 30 & 16 \\8 \mathrm{am}-12 \mathrm{pm} & 40 & 13 \\12 \mathrm{pm}-4 \mathrm{pm} & 50 & 13 \\4 \mathrm{pm}-8 \mathrm{pm} & 40 & 14 \\8 \mathrm{pm}-12 \mathrm{am} & 30 & 15\end{array}$
Enter the numbers in the appropriate cells of ranges B6:G11 and B13:G13 in the Excel spreadsheet to solve this problem based on the following formulation.
Let ^X_i ^{= number of nurses working in time period i;i = 1,6} MIN: ^1X₁ ^{+ 1X}₂ ^{+ 1X}₃ ^{+ 1X}₄ ^{+ 1X}₅ ^{+ 1X}₆
Subject to: ^1X₁ ^{+ 1X}₂ ^{? 30}
1X₂ + 1X₃ ? 40
1X₃ + 1X₄ ? 50
1X₄ + 1X₅ ? 40
1X₅ + 1X₆ ? 30
1X₁ + 1X₆ ? 20
X_i ? 0