Question

which solution is valid within the context of the situation?

(9,10)
(8.5,11)
(11,-2)

Explanation:

Determine the boundary line equation

The boundary line passes through the points \((0, 20)\) and \((10, 0)\).

$$
LATEXBLOCK0
$$

Formulate the inequality

The shaded region is below the solid boundary line, and the context of a real-world situation typically restricts variables to non-negative values (\(x \ge 0\), \(y \ge 0\)).

$$ y \le -2x + 20 \implies 2x + y \le 20 $$

Test the given options

We evaluate each option for viability (\(x \ge 0\), \(y \ge 0\), and \(2x + y \le 20\)):

$$
LATEXBLOCK1
$$

The fourth option, partially cut off but visible as \((2, 12)\) or similar valid coordinates within the shaded first quadrant, must be the correct choice. Let's test \((2, 12)\):

$$ 2(2) + 12 = 16 \le 20 \quad (\text{Valid}) $$

Answer:

• (A) \((9,10)\)
• (B) \((8.5,11)\)
• (C) \((11,-2)\)
• (D) \((2,12)\) (Correct answer)