The shaded region is the solution set of the | vedclass

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Question

(C) $1$. Analyze the line $l_1$ passing through $(0, 5)$ and $(4, 0)$. The equation of this line in intercept form is $\frac{x}{4} + \frac{y}{5} = 1$,

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) $1$. Analyze the line $l_1$ passing through $(0, 5)$ and $(4, 0)$. The equation of this line in intercept form is $\frac{x}{4} + \frac{y}{5} = 1$,which simplifies to $5x + 4y = 20$. Since the shaded region does not contain the origin $(0, 0)$,the inequality is $5x + 4y \geq 20$.$2$. Analyze the horizontal line $l_2$. The shaded region lies below the line $y = 3$,so the inequality is $y \leq 3$.$3$. Analyze the vertical line $l_3$. The shaded region lies to the left of the line $x = 6$,so the inequality is $x \leq 6$.$4$. The region is in the first quadrant,so $x \geq 0$ and $y \geq 0$.$5$. Combining these,the system of inequalities is $5x + 4y \geq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0$. This matches option $C$.

The shaded region is the solution set of the inequalities:

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