LaTex学习笔记（一）：review

95\%

b_{ij}

\begin{table}[H]
\centering
\begin{tabular}{m{100pt}<{\centering} m{100pt}<{\centering} m{200pt}<{\centering}}
\toprule
序列 &  符号& 符号说明\\midrule
  1 & $t_{ij}$ &  第i个会员第j种DVD的态度\  2 & $s_j$ & 愿意观看第j张的DVD的会员数  \  3 & $p_j$ & 会员愿意观看第j种DVD的概率  \  4 & $x_{ij}$ & 第i个会员是否被分配到第j张DVD  \  5 & $a_{ij}$ & 第i个会员对第j张DVD的满意度  \  6 & $k_{i}$ & 第i个会员有没有被分配到DVD  \  7 & $c_j$ & 第j种DVD购买的数量  \  8 & $b_{ij}$ & 第i个会员是否返还第j张DVD  \  9 & $w_j$ & 两阶段共需要购买的j种DVD数量  \  10 & $z_{ij}$ & 第二阶段针第i个会员需求的第j种DVD  \\bottomrule
\end{tabular}
\end{table}

\begin{table}[H]
\caption{会员对5种DVD的愿意观看概率}
\centering
\begin{tabular}{|c|c|c|c|c|c|}
  \hline
  $\mbox{DVD名称}$ & $\mbox{DVD1}$ & $\mbox{DVD2}$ & $\mbox{DVD3}$ & $\mbox{DVD4}$ & $\mbox{DVD5}$\  \hline
  $\mbox{第j张愿意观看概率}$ & $0.2$     & 0.1 & $0.05$  & $0.025$ & $0.01$  \  \hline
\end{tabular}
\end{table}

\begin{table}[H]
  \centering
  \caption{前30个会员分配情况}
    \begin{tabular}{r|rrr||r|rrr}
    \toprule
    会员编号 &DVD1&DVD2&DVD3& 会员编号&DVD1&DVD2&DVD3 \    \midrule
    C001  & D008  & D041  & D098  & C016  & D010  & D084  & D097 \    C002  & D006  & D044  & D062  & C017  & D047  & D051  & D067 \    C003  & D032  & D050  & D080  & C018  & D041  & D060  & D078 \    C004  & D007  & D018  & D041  & C019  & D066  & D084  & D086 \    C005  & D011  & D066  & D068  & C020  & D045  & D061  & D089 \    C006  & D019  & D053  & D066  & C021  & D045  & D050  & D053 \    C007  & D026  & D066  & D081  & C022  & D038  & D055  & D057 \    C008  & D031  & D035  & D071  & C023  & D029  & D081  & D095 \    C009  & D053  & D078  & D100  & C024  & D037  & D041  & D076 \    C010  & D041  & D055  & D085  & C025  & D009  & D069  & D094 \    C011  & D059  & D063  & D066  & C026  & D022  & D068  & D095 \    C012  & D002  & D031  & D041  & C027  & D050  & D058  & D078 \    C013  & D021  & D078  & D096  & C028  & D008  & D034  & D082 \    C014  & D023  & D052  & D089  & C029  & D026  & D030  & D055 \    C015  & D013  & D052  & D085  & C030  & D037  & D062  & D098 \    \bottomrule
    \end{tabular}%
  \label{tab:addlabel}%
\end{table}%

\begin{equation}
E=0.6*2+0.44*1=1.6
\end{equation}

\begin{equation*}
t_{ij}=
  \begin{cases}
 1,&\text{第i个会员愿意观看第j种DVD}\ 0,&\text{第i个会员不愿意观看第j种DVD}\  \end{cases}
\end{equation*}

$$s_j=\sum_{i=1}^{100000}t_{ij},j=1,2,\ldots,5$$

\begin{equation}
\lim_{n \to \infty}P(\frac{\eta_{x}-np}{\sqrt{np(1-p)}}\leq x)=\int _{-\infty}^{x}\frac{1}{\sqrt{2\pi}}e^{-\frac{t^2}{2}} dt
=\Phi (x)
\end{equation}

\par 
\newpage

\textbf{(2)三个月内95\%}

$$X=\begin{pmatrix}
x_{1,1}&x_{1,2}&\ldots&x_{1,100}\x_{2,1}&x_{2,2}&\ldots&x_{2,100}\\vdots &\vdots & &\vdots\x_{1000,1}&x_{1000,2}&\ldots&x_{1000,100}\\end{pmatrix}$$

$$ \left(\begin{array}{c}
X_1  \X_2 \\dots \X_p
\end{array}\right)
=
 \left(\begin{array}{cccc}
a_{11} & a_{12} & \dots &a_{1m} \a_{21} & a_{22} & \dots &a_{2m} \\dots & \dots & \dots &\dots \a_{p1} & a_{p2} & \dots &a_{pm} \\end{array}\right)
 \left(\begin{array}{c}
F_1  \F_2 \\dots \F_m
\end{array}\right)
\left(\begin{array}{c}
\varepsilon_1  \\varepsilon_2 \\dots \\varepsilon_p
\end{array}\right)
$$

\quad

\begin{center}
$$max\sum\limits_{i=1}^{1000}\sum\limits_{j=1}^{100} = x_{ij}a_{ij} $$
\begin{equation*}
s.t.
\begin{cases}
\sum\limits_{j=1}^{100}x_{ij} = 3k_{i}\\sum\limits_{i=1}^{1000}x_{ij} \leq num_j,j = 1,2,\ldots,100 \x_{ij},k_{ij} = 0 \text{或} 1;  \i = 1,2,\ldots,1000;  \j = 1,2,\ldots,100  \\end{cases}
\end{equation*}
\end{center}

\widehat{D_t}

\bibitem{1}

\zihao{5}\songti\thesection {附录1 \quad  第二题lingo实现代码}
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