2. This question should be answered on the sheet provided.
A builder is going to put up houses on a plot of land of area \(12000 \mathrm {~m} ^ { 2 }\).
There are 5 designs to choose from and no more than one of each design can be built.
| Design | Kendal | Milverton | Arlington | Elford | Grosvenor |
| Plot area ('000 \(\mathrm { m } ^ { 2 }\) ) | 3 | 11 | 3 | 5 | 10 |
| Value ( \(\pounds ^ { \prime } 000 \mathrm {~s}\) ) | 100 | 190 | 40 | 80 | 120 |
The builder needs to work out which houses he should build in order to maximise the total value of the site. He does this using a tree diagram and each "branch" on the tree is terminated when the total area of land on that branch exceeds \(12000 \mathrm {~m} ^ { 2 }\).
- Complete the tree diagram so that each branch is terminated or all choices have been considered.
- Hence, determine which designs the builder should use and the total value that the site will have when completed.
- Explain how this method could be altered if more than one of each design is allowed.