---
lang: ja
tags: MTNS_2024, lecture
---
# 2024年度 交通社会システム 課題1:単体法の復習<br>
## 課題1-1 | Exercise 1
以下の問題を**単体法**で解け．
Solve the following problem by using the simplex method.
$$
\begin{alignat}{6}
\displaystyle \max_{x_{1}, x_{2}, x_{3}} \quad &x_{1} &+&x_{2}&+&2x_{3}&=&z\\
\text{s.t.} \quad
& &&x_{2}&+&2x_{3}&\leq&3\\
-&x_{1}&&&+&3x_{3}&\leq&2\\
&2x_{1}&+&x_{2}&+&x_{3}&\leq&1\\
& x_{1}&,&x_{2} &,& x_{3}&\geq& 0
\end{alignat}
$$

## 課題1-2 | Exercise
次の問題を**二段階単体法**で解け：
Solve the following problem by using the two-phase simplex method.
$$
\begin{alignat}{4}
\max_{x_{1}, x_{2}, x_{3}} \quad & & 3x_{1} &+&4 x_{2} &+& 5 x_{3} &=&z\\
\text{s.t.} \quad
&& x_{1} &+&2x_{2}&+&2x_{3}&\leq&1\\
&-&3x_{1} &&&+&x_{3}&\leq&-1\\
&-&2x_{1} &-&x_{2}&&&\leq&-1\\
&&x_{1}&,&x_{2}&,&x_{3}&\geq&0
\end{alignat}
$$