function min/max value (using geometric interpretation)

**Bernice** · May 14th 2009, 02:39 PM

a) Find function $f=(x_1-4)^2+(x_2-3)^2$ ,where $x_1, x_2\ge 0$ and restrictions are: $\begin{cases} 2x_1+3x_2\ge 6 \\ 3x_1-2x_2\le 18\\ -x_1+2x_2\le8 \end{cases}$
min and max value using task geometric interpretation.

b) Find: $max f=3x_1+4x_2$ ,where $x_1, x_2\ge 0$ and restrictions are:
$\begin{cases} x_1^2+x_2^2\le 25 \\ x_1 * x_2\ge 4 \end{cases}$
using geometric interpretation.

**CaptainBlack** · May 15th 2009, 11:59 PM

Originally Posted by Bernice

a) Find function $f=(x_1-4)^2+(x_2-3)^2$ ,where $x_1, x_2\ge 0$ and restrictions are: $\begin{cases} 2x_1+3x_2\ge 6 \\ 3x_1-2x_2\le 18\\ -x_1+2x_2\le8 \end{cases}$
min and max value using task geometric interpretation.

Your objective is:

$r^2= f=(x_1-4)^2+(x_2-3)^2$

So your question is asking you to find the point in the feasible region furtherest from (4,3) and evaluate the objective there.

CB

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