A project involves four activities A$1,$ A$2,$ A$3$ and A$4.$ Characteristics of these activities are as follows:

$$ A$1$: This activity requires $50$ units of work to be completed. A worker can complete $2$ units of work in a day.

$$ A$2$: This activity requires $75$ units of work to be completed. A worker can complete $3$ units of work in a day.

$$ A$3$: This activity requires $60$ units of work to be completed. A worker can complete $4$ units of work in a day.

$$ A$4$: This activity requires $11$ units of work to be completed. A worker can complete $1$ unit of work in a day.

A$1,$ A$2$ and A$3$ can be scheduled in parallel or in any sequence. However, activity A$4$ can be started only after the activities A$1,$ A$2$ and A$3$ are completed. No activity can be completed within a fraction of a day, that is$,$ workers doing an activity will be released only at the end of the day and not in between. All the activities have to be completed within $7$ days. A worker is paid Rs$.500$ per day for all the days for the entire duration of the project, including any days the worker is idle. Work out the schedule such that the labour cost is the minimum.

The number of workers required: