7. Mrs. Hartley organises the tennis fixtures for her school. On one day she has to send a team of 10 players to a match against school \(A\) and a team of 6 players to a match against school \(B\). She has to select the two teams from a squad that includes 7 players who live in village \(C\), 5 players who live in village \(D\) and 8 players who live in village \(E\).
Having a small budget, Mrs. Hartley wishes to minimise the total amount spent on travel. The table below shows the cost, in pounds, for one player to travel from each village to each of the schools they are competing against.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | \(A\) | \(B\) |
| \(C\) | 2 | 3 |
| \(D\) | 2 | 5 |
| \(E\) | 7 | 6 |
- Use the north-west corner rule to find an initial solution to this problem.
- Obtain improvement indices for this initial solution.
- Use the stepping-stone method to obtain an optimal solution and state the pattern of transportation that this represents.
\section*{Please hand this sheet in for marking}
| Stage | State | Action | | |
| \multirow[t]{2}{*}{1} | G | GI | | |
| H | HI | | |
| \multirow[t]{3}{*}{2} | D | | | |
| E | | | |
| F | | | |
| \multirow[t]{3}{*}{3} | A | | | |
| B | | | |
| C | | | |
| 4 | Home | | | |
\includegraphics[max width=\textwidth, alt={}, center]{4e50371b-0c1c-4b4e-b21d-60858ae160df-8_662_1025_529_440}- Sheet for answering question 6 (cont.)