The shaded region in the figure is the solution set of the inequations.

5 x + 4 y \geq 20, x \leq 6, y \geq 3, x \geq 0, y \geq 0

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5 x + 4 y \leq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0

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5 x + 4 y \geq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0

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5 x + 4 y \geq 20, x \geq 6, y \leq 3, x \geq 0, y \geq 0

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Solution

The correct option is C $5 x + 4 y \geq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0$
Equation of the line passing through (0,5) and (4,0) would be -

$\frac{5 - 0}{0 - 4} = \frac{y - 0}{x - 4} \Rightarrow 5 x + 4 y = 20$
Since, the shaded region is on the right side of this line implies that the inequation should satisfy all the values of $x$ and $y$ in that region. Therefore the inequation of the line would be $5 x + 4 y \geq 20$ . And equation of line passing through $(6, 0)$ and $(6, 3)$ would be $x = 6$ and since the shaded region is on its left side, the inequation should satisfy all the values of $x$ and $y$ in that region. Therefore, the inequation would be $x \leq 6$ . Similarly the other set of inequations, would be $y \leq 3, x \geq 0 and y \geq 0.$

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