From 9b7c783f1fd590f4e2f2209a4871cee84ee569ec Mon Sep 17 00:00:00 2001
From: Koen van der Heijden <koen.vd.heijden1@gmail.com>
Date: Mon, 12 Dec 2016 01:09:59 +0100
Subject: solution job sched

---
 part1.tex | 45 ++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 40 insertions(+), 5 deletions(-)

diff --git a/part1.tex b/part1.tex
index 94aace6..420d7fb 100644
--- a/part1.tex
+++ b/part1.tex
@@ -47,10 +47,9 @@ be in the same truck.
 % combination: they are not allowed to be put in the same truck.
 
 \subsection*{Solution:}
-\begin{itemize}
- \item[(a)]
- \item[(b)]
-\end{itemize}
+\subsubsection*{(a)}
+
+\subsubsection*{(b)}
 
 
 \section*{Problem: Chip design}
@@ -139,15 +138,51 @@ We also reformed all previously mentioned requirements into formula's that can b
 (=> (<= j10 j7) (<= (+ j10 15) j7))
 \end{lstlisting}
 
+The complete scheduling output, where an integer represents the time at which a job was started is as follows:
+\begin{lstlisting}
+j1 -> 1
+j2 -> 0
+j3 -> 7
+j4 -> 0
+j5 -> 15
+j6 -> 0
+j7 -> 25
+j8 -> 15
+j9 -> 28
+j10 -> 0
+j11 -> 15
+j12 -> 42
+\end{lstlisting}
+
+Note that $42 + 12 + 5$ is indeed equal to $59$.
+
 \subsubsection*{(b)}
 This solution was retrieved in the same way as answer a. This answer is $m = 65$.
-2 extra lines were added to ensure that job 6 lies withing job 12:
+2 extra lines were added to ensure that job 6 lies within job 12:
 
 \begin{lstlisting}
 (>= j6 j12)
 (<= (+ j6 11) (+ j12 17))
 \end{lstlisting}
 
+With those 2 extra formula lines, the new schedule becomes:
+
+\begin{lstlisting}
+j1 -> 1
+j2 -> 0
+j3 -> 7
+j4 -> 0
+j5 -> 15
+j6 -> 42
+j7 -> 53
+j8 -> 15
+j9 -> 28
+j10 -> 0
+j11 -> 15
+j12 -> 42
+\end{lstlisting}
+Note that $53 + 7 + 5$ is indeed equal to $65$.
+
 \section*{Problem: Integer sum from neighbors}
 Eight integer variables $a_1$, $a_2$, $a_3$, $a_4$, $a_5$, $a_6$, $a_7$, $a_8$
 are given, for which the initial value of
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