# Dynamic Programming

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

DP Formulation:....

Min

s.t.

Stage 1:

Stage 2:

Stage 3:

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#### Solution Preview

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.

Solution:

Since the decision variables are x1, x2 and x3, the given problem is a three-stage problem defined as follows:

s3=3x1+2x2+x3 â‰¥ 18

s2=3x1+2x2=s3-x3

s1=3x1=s2-2x2

Therefore the functional (recurrence) relation is

f1(s1) = min (3x12) = (s2-2x2)2

0â‰¤x1â‰¤s1

f2(s2) = min (3x12+x22) = min ...

#### Solution Summary

A dynamic programming problem is solved. The solution is comprehensive and well presented.