1 D aniel needs to clean four houses but only has one day in which to do it. He estimates that each house will take one day and so he has asked three professional cleaning companies to give him a quotation for cleaning each house. He intends to hire the three companies to clean one house each and he will clean the fourth house himself. The table below shows the quotations that Daniel was given by the three companies.
| House 1 | House 2 | House 3 | House 4 |
| Allclean | \(\pounds 500\) | \(\pounds 400\) | \(\pounds 700\) | \(\pounds 600\) |
| Brightenupp | \(\pounds 300\) | \(\pounds 200\) | \(\pounds 400\) | \(\pounds 350\) |
| Clean4U | \(\pounds 500\) | \(\pounds 300\) | \(\pounds 750\) | \(\pounds 680\) |
- Copy the table and add a dummy row to represent D aniel.
- A pply the Hungarian algorithm, reducing rows first, to find a minimum cost matching. You must show your working and say how each matrix was formed.
- Which house should Daniel ask each company to clean? Find the total cost of hiring the three companies.