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+++ b/slides.tex
@@ -47,21 +47,21 @@ A ride sharing company wants to send riders promotional coupons in the hope of m
 \begin{frame}{Multiple-choice knapsack}
 \textbf{Input}: $n$ sets of coupons $K_1,\dots,K_n$. Each coupon $e\in K_i$ has a non-negative cost $c_e\in \Z_+$ and value $v_e\in \Z_+$. A positive budget $b\in \Z_+$.
 
-\textbf{Output}: A subset of coupons $K$ that maximizes the total value $\sum_{e\in K} c_e$ while satisfying \textcolor{Red}{$|K\cap K_i|\leq 1$} and $\sum_{e\in K} c_e\leq b$.
+\textbf{Output}: A subset of coupons $K$ that maximizes the total value $\sum_{e\in K} v_e$ while satisfying \textcolor{Red}{$|K\cap K_i|\leq 1$} and $\sum_{e\in K} c_e\leq b$.
 
 \vspace{1em}
 \pause
 
-Three problems with this modeling:
+Three problems with this formulation:
 \begin{enumerate}
 \item Finding the exact optimum is NP-hard. So we consider solving it approximately.
 \item Companies may run multiple campaigns at the same time. So a trade-off curve between budget and profit will be useful.
-\item The multiple-choice constraint \textcolor{Red}{$|K\cap K_i|\leq 1$} is too weak for real applications.
+\item The multiple-choice constraint \textcolor{Red}{$|K\cap K_i|\leq 1$} is too weak for real-world applications.
 \end{enumerate}
 
 \end{frame}
 
-\begin{frame}{Linear programming formulation}
+\begin{frame}{Linear programming relaxation}
 \textcolor{gray}{
 \textbf{Input}: $n$ sets of coupons $K_1,\dots,K_n$. Each coupon $e\in K_i$ has a non-negative cost $c_e\in \Z_+$ and value $v_e\in \Z_+$. \st{A positive budget $b\in \Z_+$.}
 }