4.

$$\begin{array} { l l l l l l l l l l l } 
25 & 9 & 32 & 16 & 17 & 23 & 18 & 12 & 4 & 8 & 40
\end{array}$$

The numbers in the list represent the weights, in kilograms, of eleven suitcases. The suitcases are to be transported in containers that will each hold a maximum weight of 50 kg .
\begin{enumerate}[label=(\alph*)]
\item Calculate a lower bound for the number of containers needed. You must make your method clear.
\item Use the first-fit bin packing algorithm to allocate the suitcases to the containers.
\item Carry out a quick sort to produce a list of the weights in descending order. You should show the result of each pass and identify your pivots clearly.
\item Use the first-fit decreasing bin packing algorithm to allocate the suitcases to the containers.

The two heaviest suitcases are replaced with two suitcases both of which weigh $x \mathrm {~kg}$. It is given that the lower bound for the number of containers needed is now one less than the number found in (a).
\item Determine the range of values for $x$. You should make your working clear.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2019 Q4 [15]}}