Check if the given vectors are optimal solutions of the corresponding problems. 1. XI + 4X2 + X3 → max. 4X1 + 11X2 + 3X3 7, rI X2-X3=0, X1+ 13, .y20, j = 1.2.3. Check if the given vectors are op...

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Check if the given vectors are optimal solutions of the corresponding problems. 1. XI + 4X2 + X3 → max. 4X1 + 11X2 + 3X3 7, r

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Answer 1

Answer #1

No, the following vector is not an optimal solution, since it is not maximizing the function.

Reason: The Maxima exists at

$2 2 0$

It satisfies the constraints

$4(0) + 11(\frac{1}{2}) + 3(\frac{1}{2}) = 7, 0 + \frac{1}{2} - \frac{1}{2} = 0$

The value occurring at the vector [0,1/2,1/2] will be

$0 + 4(\frac{1}{2}) + \frac{1}{2} = 2.5$

The given vector solution [1,0,1] will be having the value of

$1 + 0 + 1 = 2$

which is less than the value of 2.5

Hence, it is not the optimal solution

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Answer 2

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