Question 5 Answer & Explanation - SAT Algebra

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algebra

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

$26$

$30$

$28$

$0$

Correct Answer: A

Choice A is the correct answer. Test the vertices.

(0, 6): $C = 4(0) + 5(6) = 30$
(4, 2): $C = 4(4) + 5(2) = 16 + 10 = 26$
(7, 0): $C = 4(7) + 5(0) = 28$
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.

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