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practice testMultiple Choice

Practice Test

Question 2 • Algebra 2 with Probability

The constraints of a problem are listed. What are the vertices of the feasible region? x plus y is less than or equal to 5 y is less than or equal to 3 x is greater than or equal to 0 y is greater than or equal to 0

Answer
A
open paren 0 comma 0 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
B
open paren 0 comma 0 close paren , open paren 0 comma 3 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
C
open paren 0 comma 3 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren
D
open paren 0 comma 0 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren

Explanation

The constraints keep the region in the first quadrant, below y = 3, and below x + y = 5. On the y-axis, the boundary points are (0, 0) and (0, 3). The lines y = 3 and x + y = 5 intersect at (2, 3), and x + y = 5 meets the x-axis at (5, 0). Thus the vertices are (0, 0), (0, 3), (2, 3), and (5, 0), which matches choice B.

AI-written and checked against the verified answer.

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