$2.$ Consider the following project flow diagram.

Recall: Flow times for each activity are listed above the activity. The arrows represent which activities need to be finished before others can start, e$.$g$.,$ A must come before $\backslash ($ C $\backslash ),$ but $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ can happen simultaneously.

The following table contains information about how much each activity costs. The table also contains information about crash times and crash costs.

$($a$)$ What is the critical path in the project?

$($b$)$ What is the current duration of the process? $($i$.$e$.,$ without any crashing?$)$

$($c$)$ Complete the following table to compute the cost slopes:

$($d$)$ If the original activity times are used, then it will cost a total of $\backslash (\backslash$$ $50\backslash )$ to complete all activities $($i$.$e$.,$ a total of $\backslash (\backslash$$ $50\backslash )$ to complete the project$).$ What is the minimum amount of extra money you need to spend in order to reduce the project duration by $2$ minutes?

Answer in dollars. For instance, if you reduce the project duration by $2$ minutes and it now costs a total of $\backslash (\backslash$$ $120\backslash )$ to complete all activities $($i$.$e$.,$ a total of $\backslash (\backslash$$ $120\backslash )$ to complete the project based on the reduced times$),$ then you will pay an extra $\backslash (\backslash$$ $120-\backslash$$ $50=\backslash$$ $70\backslash ).$ Hence, you would write $\backslash (\backslash$$ $70\backslash ).$