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\title{37335 - Differential Equations Assignment}
\author{Jack Macdessi - ????????}
\author{Raymond Sok - 25347891}
\author{Zachary Zerafa - 24557656}

\begin{document}

\maketitle

\vspace{0.5in}

\section{Part A}
\subsection{Problem Introduction}
- describe process of translating a problem into LP
\subsection{Problem Settings}
$r$ - standard hourly rate
$r^{*}$ - overtime hourly rate
$r^{*}$ - overtime hourly rate
\subsection{Decision Variables}
- signifies amount of workers for each combination of all shift possibilities for a nurse, denote this as a 'shift-type'
- 8 possible shift-types
$p_i$ - nurses working during 6-hour period i
$s_{i,k}$ - nurses working the shift starting at 6-hour period i for a duration of k hours, where k=12 or k=18
\subsection{Objective Function}
- signifies 'cost function' relating the cost of having a certain amount of nurses in each shift-type
\subsection{Constraints}
- ensures that the minimum amount of nurses per 6-hour period is satisfied
- each 6-hour period is covered by 5 shift-types, this is used to translate the notion of 'shift-types' to nurses working within an arbitrary 6-hour period
\subsection{Organization in Microsoft Excel\texttrademark}
- problem settings (blue)
- decision variables (orange)
- nurses working within the ith 6-hour period (green)
- objective function (???)
- briefly mention use of integer simplex method
\subsection{Results}
- state results in a table
- consider ratio of 12-hour shifts to 18-hour shifts
- consider how the optimal amount of nurses per shift finance-wise equals the lower bound for nurses per 6-hour period
\chapter{Part B}
\section{Principles of Ethical Engagement}

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