Solving the software project scheduling problem is to find a good allocation of employees to tasks in a software project so as to minimize its cost and duration. Assume we have been given $n$ employees $e_1,$dots,$e_n$ with $m$ tasks $t_2,$dots,$t_m.$ We then formulate a matrix $x^{\text{'}}$ of employees by tasks. The following shows the variables and initial calculation on durations $($p$-$month $-$ person$-$month$)$:

$($a$)$ What is the normalised dedication of the employees to tasks during the period of time that would have had overwork?

$[2$ marks$]$

$($b$)$ If we use the evolutionary algorithm design explained in this module, what would be the duration of the project?

$[18$ marks$]$