AnswersAlgebra 2 with ProbabilitySystems of Equations and Inequalities — TestQuestion 6
6
QuizMultiple Choice

Systems of Equations and Inequalities — Test

Question 6 • Algebra 2 with Probability

Joey is buying plants for his garden. He wants to have at least twice as many flowering plants as nonflowering plants and a minimum of 36 plants in his garden. Flowering plants sell for 8 dollars , and nonflowering plants sell for 5 dollars Joey wants to purchase a combination of plants that minimizes cost. Let x represent the number of flowering plants and y represent the number of nonflowering plants. What are the vertices of the feasible region for this problem?

Answer
A
open paren 0 comma 36 close paren , open paren 24 comma 12 close paren , open paren 36 comma 0 close paren
B
open paren 0 comma 0 close paren , open paren 0 comma 36 close paren , open paren 24 comma 12 close paren
C
open paren 0 comma 36 close paren , open paren 24 comma 12 close paren
D
open paren 24 comma 12 close paren , open paren 36 comma 0 close paren

Explanation

The constraints are x ≥ 2y, x + y ≥ 36, and x,y ≥ 0. The boundary lines x = 2y and x + y = 36 intersect at (24, 12). On the x-axis, y = 0, so the minimum-total boundary x + y = 36 meets it at (36, 0). These are the two vertices of the feasible region, so the correct choice is (24, 12) and (36, 0).

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