Set 7: Linear Inequalities (Intermediate)

Explanation

Answer: A

Find the minimum value of $C = 4x + 5y$ in the region with vertices $(0, 6)$ , $(4, 2)$ , and $(7, 0)$ bounded by $x, y \geq 0$ .

$26$

✓ Correct

$30$

$28$

$0$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Test the vertices. 1. (0, 6): $C = 4(0) + 5(6) = 30$ 2. (4, 2): $C = 4(4) + 5(2) = 16 + 10 = 26$ 3. (7, 0): $C = 4(7) + 5(0) = 28$ 4. Minimum: 26 is the lowest value. Strategic Tip: Don't assume the vertex closest to the origin is the minimum; coefficients matter. Choice B is incorrect because 30 is the maximum. Choice C is incorrect because 28 is not the minimum. Choice D is incorrect because $(0,0)$ is not a vertex of this region.

Key Steps:

•

The correct answer is $26$

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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