1

Set 3: Linear Inequalities (Advanced)

Explanation

Answer: A

Maximize P=5x+3yP = 5x + 3y given vertices (0,0),(6,0),(4,4),(0,5)(0,0), (6,0), (4,4), (0,5).

A.

3232

✓ Correct
B.

3030

C.

1515

D.

2020

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Test all vertices. 1. (0,0): 00 2. (6,0): 5(6)+3(0)=305(6) + 3(0) = 30 3. (4,4): 5(4)+3(4)=20+12=325(4) + 3(4) = 20 + 12 = 32 4. (0,5): 5(0)+3(5)=155(0) + 3(5) = 15 5. Maximum: 32 Strategic Tip: The maximum isn't always at the axis intercepts. Choice B is incorrect because 30 is less than 32. Choice C is incorrect because 15 is less than 32. Choice D is incorrect because 20 is less than 32.

Key Steps:

•

The correct answer is 3232

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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