A project involves three activities $a_1, a_2$ and $a_3$. $a_3$ can start only after $a_1, a_2$ are completed. The amount of work done by a single worker in a day for the activities are 2, 3 and 1 units respectively. The total amount of work for the activities are 4,3 and 30 units respectively. The total number of workers available are 15. How many workers should be assigned to activity 1 such that the total time taken for the project is minimum.
I tried to formulate the optimization problem but I'm stuck at mathematicalizing the constraints. I don't know how to put the constraint "$a_3$ can start only after $a_1, a_2$ are completed" in a mathematical form.
