Help me answer question number 5
5.
We define states 1, 2 and 3 as follows.
= units of resource associated to activity 1
= units of resource associated to activities 1 and 2
= units of resource associated to activities 1, 2 and 3
Calculation for first stage (activity 1)-
Available units of resource () | Total profit in activity 1 |
0 | 0 |
1 | 8 |
2 | 18 |
3 | 22 |
4 | 24 |
Calculation for second stage (activities 1 & 2)-
Best profit for activities 1 and 2 = Max { Profit of the feasible alternatives for activity 2 + best profit for stage 1 }
Available units of resource () | Total profit in activities 1 & 2 | Resource allotted for activity 2 |
0 | max {0+0}=0 | 0 |
1 | max{0+8,3+0}=8 | 0 |
2 | max{0+18,3+8,6+0}=18 | 0 |
3 | max{0+22,3+18,6+8,9+0}=22 | 0 |
4 | max{0+24,3+22,6+18,9+8,12+0}=25 | 1 |
Calculation for third stage (activities 1, 2 & 3)-
Best profit for activities 1, 2 and 3 = Max { Profit of the feasible alternatives for activity 3 + best profit for stage 2 }
Available units of resource () | Total profit in activities 1, 2 & 3 | Resource allocated for activity 3 |
4 | max{0+25,6+22,7+18,8+8,10+0}=28 | 1 |
So, to obtain the solution of the dynamic programming problem we observe as follows.
Our solution is to allocate 3, 0 and 1 units of resource in activities 1, 2 and 3 respectively. (Which gives maximised profit 28)
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