Explanation:
(D) : Given,
\(\mathrm{z}=10 \mathrm{x}+\mathrm{y}\) subject to \(\mathrm{x} \leq 4, \mathrm{y} \leq 6, \mathrm{x}+\mathrm{y} \leq 6, \mathrm{x} \geq 6, \mathrm{x}\) \(\geq 0, \mathrm{y} \geq 0\)
Using graphical method we get.

Point \(B\) is calculated as follows solve \(x=4\) and \(x+y=6\)
We get \(y=2\) so the corner point \(B\) is given as \((4,2)\),
There solve, corner points A, B, C and D are A \((0,6)\)
\(B(4,2) C(4,0)\) and \(D(0,0)\) Now, value of \(z\) at
There corner points \(\mathrm{z}=10 \mathrm{x}+\mathrm{y}\)
At Point \(\mathrm{A}, \mathrm{z}=6\)
At Point B, \(z=10 \times 4+2=42\)
At Point \(\mathrm{C}, \mathrm{z}=40\)
At point \(\mathrm{D}, \mathrm{z}=0\)
\(\therefore\) The maximum valve is 42