Question

which solution is valid within the context of the situation?

(19,6)
(17.5,5)
(30,-10)
(10,15)

Explanation:

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<reasoning>

Identify the constraints from the graph

\[

$$\begin{aligned} &\text{Feasible region is shaded in the first quadrant (dark grey region).}\\ &x \ge 0, \quad y \ge 0 \quad (\text{Real-world context requires non-negative values}) \end{aligned}$$

\]

Evaluate the given options against constraints

\[

$$\begin{aligned} &(30, -10): \quad y = -10 < 0 \quad (\text{Invalid})\\ &(10, 15): \quad \text{Located well above the shaded region boundary}\\ &(17.5, 5): \quad \text{Non-integer values; real-world context typically requires integers}\\ &(19, 6): \quad \text{Lies within the shaded region; consists of valid whole numbers} \end{aligned}$$

\]

Confirm the valid solution

\[
(x, y) = (19, 6)
\]
</reasoning>

<answer>
<mcq-correct>(A) (19,6)</mcq-correct>
<mcq-option>(B) (17.5,5)</mcq-option>
<mcq-option>(C) (30,-10)</mcq-option>
<mcq-option>(D) (10,15)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the constraints from the graph

\[

$$\begin{aligned} &\text{Feasible region is shaded in the first quadrant (dark grey region).}\\ &x \ge 0, \quad y \ge 0 \quad (\text{Real-world context requires non-negative values}) \end{aligned}$$

\]

Evaluate the given options against constraints

\[

$$\begin{aligned} &(30, -10): \quad y = -10 < 0 \quad (\text{Invalid})\\ &(10, 15): \quad \text{Located well above the shaded region boundary}\\ &(17.5, 5): \quad \text{Non-integer values; real-world context typically requires integers}\\ &(19, 6): \quad \text{Lies within the shaded region; consists of valid whole numbers} \end{aligned}$$

\]

Confirm the valid solution

\[
(x, y) = (19, 6)
\]
</reasoning>

<answer>
<mcq-correct>(A) (19,6)</mcq-correct>
<mcq-option>(B) (17.5,5)</mcq-option>
<mcq-option>(C) (30,-10)</mcq-option>
<mcq-option>(D) (10,15)</mcq-option>
</answer>

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