Can budget lines be discontinuous?
I guess the discount holds for the 100 first units of food even if she buys more than 100. Therefore the new budget line is
\begin{equation*}
\left\{
   \begin{array}{ll}
   &amp; 200 = 0.2 F + 2C \text{ if } F &lt; 100 \\
   &amp; 200 = 0.2 \times 100 + F-100+2C \text{ otherwise }
   \end{array}
\right.
\end{equation*}
which is continuous.