Question $5$ A

Consider a modified version of the Activity Selection problem in which each activity $a_i$ has a profit $p_i,$ in addition to a start time $s_i$ and finish time $f_i.$ The goal is no longer to maximize the number of activities scheduled, but instead to maximize the total profit of the activities scheduled. That is$,$ we wish to choose a set $A$ of mutually compatible activities such that ${\displaystyle \underset{\text{j}\text{i}\text{n}\text{A}}{\overset{?}{}}}{p}_j$ is maximized.

For example, given four jobs with the following start time, finish time, and profit values,

$\backslash$table$[[i,1,2,3,4$