# Thread: Linear programming (maximizing)

1. ## Linear programming (maximizing)

I am not sure whether I have done this right or that my answer is correct. I have a strong feeling that tells me it is not right. Could you please check it for me?

Minimize
C = x + y
subject to the constraints
1x +7y ≥ 1
11x + 2y ≥ 1
x, y ≥ 0

The answers I got through solving the system geometrically/graphically is that the minimum of C is 0.244360901 and occurs when x = 0.11842105 and y = 0.125939849.

2. ## Re: Linear programming (maximizing)

Hello, Yoodle15!

I have no idea how you got those ugly decimals . . .

$\text{Minimize: }\:C \:=\: x + y$

$\text{Subject to the constraints: }\:\begin{Bmatrix}x +7y \:\ge\:1 \\ 11x + 2y \:\ge\:1 \\ x, y\:\ge\: 0\end{Bmatrix}$

$\text{The graph looks like this:}$

Code:
      |::::::
|::::::::
Ro:::::::::
|*:::::::::
| *:::::::::
|  *:::::::::
*   *:::::::::
|  * *:::::::::
|     o::::::::::
|    Q * *::::::::
|       *   *:::::::
|        *     *:::::::
- + - - - - * - - - o - - - -
|                 P
$\text{The vertices are: }\:\begin{Bmatrix}P: &(1,0) \\ \\[-4mm] Q: & (\frac{2}{15},\frac{1}{15}) \\ \\[-4mm] R: & (0,\frac{1}{2}) \end{Bmatrix}$

$\text{Test them in the }C\text{-function.}$