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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.

Task $T_1$ $T_2$ $T_3$ $T_4$ $T_5$ $T_6$ $T_7$ $T_8$ $T_9$
Profit 15 20 30 18 18 10 23 16 25
Deadline 7 2 5 3 4 5 2 7 3

What is the maximum profit earned?

1. 147
2. 165
3. 167
4. 175
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15 + 20 +30 +18 + 16 + 23 + 25 = 147

The most important statement in question is

each task requires one unit of time

This shows that we can greedily choose the better task and that should give us the optimal solution. The best task would be the one with maximum profit. Thus we can sort the tasks based on deadline and then profit as follows:

Task T7 T2 T9 T4 T5 T3 T6 T8 T1
Deadline 2 2 3 3 4 5 5 7 7

0 --T7 -- 1  --  T2  --  2  --  T9  --  3  --  T5  --  4  --  T3 --  5 --  T8 --  6  --  T1 --  7

so we know that T4 and T6 are left

so profit will not include T4 and T6 = 15 + 20 +30 +18 + 16 + 23 + 25 = 147

answered by Veteran (48.4k points)
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answered by Boss (6.5k points)