$1.$ Formulate this scheduling problem as a CSP$.(10$ points$)$

Hints: Choose the variables to be time point at which a task is started. State the initial domain of each

variable as a set of discrete values, one value per hour. Specify the unary constraints that restrict the

start time of a task given its duration to the duration of the entire job $($i$.$e$.,$ four hours$).$ For example,

a task whose duration is $1$ hour cannot start at $$time point$4.$ Specify the binary constraints that link

the variables as an algebraic constraint. The constraint expressions we are looking for are of the form

Sb $+2<$ Sw $($this example expression is only to give you an idea of what to write: it is not one of the

constraints listed above.$)$

$2.$ Draw the complete search tree generated by a backtrack$-$search procedure with forward$-$checking using

a static variable ordering of your choice. Specify, as best you can, the domains filtered after each

forward$-$checking step