A Hospital Needs to Determine How Many Nurses to Hire

question 49

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

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Definitions:

Shipment Cost

The expenses associated with the transportation of goods from one location to another, including freight charges and packaging.

Determinants of Revenue

The factors that influence the amount of income generated from sales of goods or services, such as market demand, pricing strategies, and competition.

Service Firm

A company that provides services rather than tangible goods to consumers or other businesses.

Quality of Raw Materials

The measure of suitability, consistency, and integrity of materials sourced for manufacturing, impacting the final product's quality.