A Hospital Needs to Determine How Many Nurses to Hire

question 15

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.
$\begin{array}{lcc}\text { Time period } & \text { Required \# of Nurses } & \text { Wage }(\$ / \mathrm{hr}) \\\hline 12 \mathrm{am}-4 \mathrm{am} & 20 & 15 \\4 \mathrm{am}-8 & 30 & 16 \\\text { am } & & \\8 \mathrm{am}-12 \mathrm{pm} & 40 & 13 \\12 \mathrm{pm}-4 \mathrm{pm} & 50 & 13 \\4 \mathrm{pm}-4 & 40 & 14 \\\mathrm{pm}\\8 \mathrm{pm}-12 \mathrm{am}&30 & 15 \end{array}$

What values would you enter in the Risk Solver Platform (RSP) task pane for the following cells for this Excel spreadsheet implementation of the formulation for this problem?
Objective Cell:
Variables Cells:
Constraints Cells:
Let $\quad X _ { i } =$ mumber of nurses warking in thme period $i ; i = 1,6$
$$\begin{array} { l l } \text { MiN: } & 1 \mathbf { X } _ { 1 } + 1 \mathbf { X } _ { \mathbf { 2 } } + 1 \mathbf { X } _ { \mathbf { 3 } } + 1 \mathbf { X } _ { 4 } + 1 \mathbf { X } _ { \mathbf { 5 } } + 1 \mathbf { X } _ { \mathbf { 6 } } \\\text { Subject ta: } & 1 \mathbf { X } _ { 1 } + 1 \mathbf { X } _ { \mathbf { z } } \geq 30 \\& 1 \mathbf { X } _ { \mathbf { 2 } } + 1 \mathbf { X } _ { \mathbf { 3 } } \geq 40 \\& 1 \mathbf { X } _ { \mathbf { 3 } } + 1 \mathbf { X } _ { 4 } \geq 50 \\& 1 \mathbf { X } _ { 4 } + 1 \mathbf { X } _ { \mathbf { 5 } } \geq 40 \\& 1 \mathbf { X } _ { 5 } + 1 \mathbf { X } _ { \mathbf { 1 } } \geq 30 \\& 1 \mathbf { X } _ { 1 } + 1 \mathbf { X } _ { \mathbf { 1 } } \geq 20 \\& \mathbf { X } _ { \mathrm { i } } \geq 0\end{array}$$

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Definitions:

Achievement Tests

Assessments designed to measure a person's knowledge or proficiency in a particular area or skill.

Biological Approach

A perspective in psychology that explains behaviors and mental states through biological factors such as genetics, brain structures, and biochemical processes.

Personality Change

Alterations in an individual's behavioral patterns, attitudes, and emotional responses over time.

BAS

Behavioral Activation System, which is a neurological system thought to regulate motivation towards rewards and positive reinforcement.