# function min/max value (using geometric interpretation)

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• May 14th 2009, 03:39 PM
Bernice
function min/max value (using geometric interpretation)
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.
• May 16th 2009, 12:59 AM
CaptainBlack
Quote:

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