Please see the attached file for the fully formatted problem.
Use Dynamic Programming to solve:
1. Min f(x-bar) = 3x21 + x22 + 2x23
s.t. Sx1 + 2x2 +x3 >= 18
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I have provided a detailed solution for your problem. I have also checked your partial solution. I found at two places your first order differentiation to find the minimum value was wrong. I have indicated it with red arrows. I have used different notations at some places.
Please find attached 1) Solution for the given problem
2) Your question file with some corrections.
Since the decision variables are x1, x2 and x3, the given problem is a three-stage problem defined as follows:
s3=3x1+2x2+x3 ≥ 18
Therefore the functional (recurrence) relation is
f1(s1) = min (3x12) = (s2-2x2)2
f2(s2) = min (3x12+x22) = min ...
A dynamic programming problem is solved. The solution is comprehensive and well presented.