- A team of gardeners is called in to attend to the grounds of a stately home. The three gardeners will each be assigned to one of three areas, the lawns, the hedgerows and the flower beds. The table below shows the estimated time, in hours, it will take each gardener to do each job.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Lawns | Hedgerows | Flower Beds |
| Alan | 4 | 4.5 | 6 |
| Beth | 3 | 4 | 5 |
| Colin | 3.5 | 5 | 6 |
The team wishes to complete the tasks in the least total time.
Formulate this information as a linear programming problem.
- State your decision variables.
- Write down the objective function in terms of your decision variables.
- Write down the constraints and explain what each one represents.