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The shaded region in the figure is the solution set of the inequations
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\( 4 x+5 y \geq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0 \)
Equation of line \(A B: \frac{x}{5}+\frac{y}{4}=1 \Rightarrow 4 x+5 y=20\)
Equation of line CD: \(\frac{\mathrm{x}}{10}+\frac{\mathrm{y}}{3}=1 \Rightarrow 3 \mathrm{x}+10 \mathrm{y}=30\)
Equation of line \(\mathrm{EF}: \mathrm{x}=6\)
Here we can see the shaded area above the line \(A B\), Below the line \(C D\) and Left of line EF
\(\therefore 4 x+5 y \geq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0\)
Equation of line CD: \(\frac{\mathrm{x}}{10}+\frac{\mathrm{y}}{3}=1 \Rightarrow 3 \mathrm{x}+10 \mathrm{y}=30\)
Equation of line \(\mathrm{EF}: \mathrm{x}=6\)
Here we can see the shaded area above the line \(A B\), Below the line \(C D\) and Left of line EF
\(\therefore 4 x+5 y \geq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0\)
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