# Question #0cfc6

Mar 14, 2017

Minimum value: $\left(- 9\right)$

#### Explanation:

Note that $C = - 2 x + y$ is linear so its maximum and minimum values will occur at the boundary limits for $x$ and $y$

For the minimum value of $C$
each of the terms must be minimum;

that is:
we need the minimum value of $\left(- 2 x\right)$
$\textcolor{w h i t e}{\text{XXX}}$ with $x \in \left[- 5 , 4\right]$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = 4$
and the minimum value of $y$
$\textcolor{w h i t e}{\text{XXX}}$ with $y \in \left[- 1 , 3\right]$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = - 1$

If $\left(x , y\right) = \left(4 , - 1\right)$
then $C = \left(- 2\right) \cdot 4 + \left(- 1\right) = - 9$