The shaded region in the figure is the soluti | vedclass

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Question

(C) $1$. Identify the equations of the lines from their intercepts:- Line passing through $(0, 4)$ and $(5, 0)$: $\frac{x}{5} + \frac{y}{4} = 1 \Right

Vedclass · Accepted Answer

$4x + 5y \geq 20, 3x + 10y \leq 30, x \leq 6, x, y \geq 0$

Vedclass · Answer

(C) $1$. Identify the equations of the lines from their intercepts:- Line passing through $(0, 4)$ and $(5, 0)$: $\frac{x}{5} + \frac{y}{4} = 1 \Rightarrow 4x + 5y = 20$.- Line passing through $(0, 3)$ and $(10, 0)$: $\frac{x}{10} + \frac{y}{3} = 1 \Rightarrow 3x + 10y = 30$.- Vertical line passing through $(6, 0)$: $x = 6$.$2$. Determine the inequalities based on the shaded region:- The shaded region is above the line $4x + 5y = 20$,so the inequality is $4x + 5y \geq 20$.- The shaded region is below the line $3x + 10y = 30$,so the inequality is $3x + 10y \leq 30$.- The shaded region is to the left of the line $x = 6$,so the inequality is $x \leq 6$.- Since the region is in the first quadrant,$x, y \geq 0$.Thus,the correct set of inequations is $4x + 5y \geq 20, 3x + 10y \leq 30, x \leq 6, x, y \geq 0$.

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

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