A community is currently being served by a single self-serve gas station with six pumps. A competitor is opening a new facility with 12 pumps across town. The table below shows the travel times in minutes from the four different areas in the community to the sites and the number of customers in each area.

a. Using the Huff retail location model and assuming that lambda=2, calculate the probability of a customer traveling from each area to each site.

b. Estimate the proportion of the existing market lost to the new competitor. You may assume customers spend on an average $20 at the pumping stations.

\begin{tabular}{|l||r|r|r|r|r|} \hline \multicolumn{1}{|c|}{ Area } & \multicolumn{1}{|c|}{1} & \multicolumn{1}{c|}{2} & \multicolumn{1}{c|}{3} & \multicolumn{1}{c|}{4} \\ \hline \hline Old station & 5 & 10 & 9 & 15 \\ \hline \hline New competitor & 20 & 8 & 12 & 6 \\ \hline \hline Number of customers & 100 & 150 & 80 & 50 \\ \hline \end{tabular}