Q84a

We are given $9$ tasks $T_1, T_2, \dots, T_9$. The execution of each task requires one unit of time. We can execute one task at a time. Each task $T_i$ has a profit $P_i$ and a deadline $d_i$. Profit $P_i$ is earned if the task is completed before the end of the $d_i^{th}$ unit of time.

$$\begin{array}{|l|l|l|l|l|l|l|l|l|}\hline \textbf{Task} & \text{$T_1$ } & \text{$T_2$}& \text{$T_3$} & \text{$T_4$} & \text{$T_5$} & \text{$T_6$} & \text{$T_7$} & \text{$T_8$} & \text{$T_9$} \\\hline \textbf{Profit} & \text{$15$ } & \text{$20$}& \text{$30$} & \text{$18$} & \text{$18$} & \text{$10$} & \text{$23$} & \text{$16$} & \text{$25$} \\\hline \textbf{Deadline} & \text{$7$} & \text{$2$} & \text{$5$} & \text{$3$} & \text{$4$} & \text{$5$} & \text{$2$} & \text{$7$} & \text{$3$} \\\hline \end{array}$$

Are all tasks completed in the schedule that gives maximum profit?