Given:
[tex]\begin{gathered} y\leq\frac{1}{4}x+3 \\ y\ge-x+5 \end{gathered}[/tex]
For the given inequality,
[tex]\begin{gathered} y\leq\frac{1}{4}x+3 \\ \text{for x=0}\Rightarrow y=3 \end{gathered}[/tex]
So, this inequality contains all the points below point (0,3). that means it contains region D and C
[tex]\begin{gathered} y\ge-x+5 \\ \text{for x=0}\Rightarrow y=5 \end{gathered}[/tex]
This inequality contains all the points above (0,5) and it will include the region B and C.
From above discussion, region C is common in both the inequalities.
Answer: option B)
