Set 1: Linear Functions (Advanced)

Explanation

Answer: A

Maximize $P = 3x + 2y$ subject to $x + y \leq 5$ , $x \geq 0, y \geq 0$ .

$15$

✓ Correct

$10$

$13$

$12$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Check vertices. 1. Vertices: $(0,0), (5,0), (0,5)$ . 2. Evaluate P: - $(0,0): 0$ - $(5,0): 3(5) + 0 = 15$ - $(0,5): 0 + 2(5) = 10$ 3. Max: 15. Strategic Tip: The maximum usually occurs at a vertex. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is $15$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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