2 Dudley has three daughters who are all planning to get married next year. The girls are named April, May and June, after the months in which they were born. Each girl wants to get married on her own birthday.
Dudley has already obtained costings from four different hotels. From past experience, Dudley knows that when his family get together they are likely to end up with everyone fighting one another, so he cannot use the same hotel twice.
The table shows the costs, in \(\pounds 100\), for each hotel to host each daughter's wedding.
| Hotel |
| \cline { 2 - 6 } | | Palace | Regent | Sunnyside | Tall Trees |
| \cline { 2 - 6 } | April | 30 | 28 | 32 | 25 |
| \cline { 2 - 6 }
Daughter | May | 32 | 34 | 32 | 35 |
| \cline { 2 - 6 } | June | 40 | 40 | 39 | 38 |
| \cline { 2 - 6 } | | | | | |
| \cline { 2 - 6 } |
Dudley wants to choose the three hotels to minimise the total cost.
Add a dummy row and then apply the Hungarian algorithm to the table, reducing rows first, to find an optimal allocation between the hotels and Dudley's daughters. State how each table is formed and write out the final solution and its cost to Dudley.