Free Printable WorksheetMathAlgebra IMath CurriculumA-CED.3

ALG1.63 Interpret Intersections and Feasible Regions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.63 Interpret Intersections and Feasible Regions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.63 Interpret Intersections and Feasible Regions - Primary standard selected for prompt fields in this prompt cell: CCSS A-CED.3. Skill statement in this prompt cell: Select the statement that correctly interprets intersection points, lines of intersection, and boundary lines in context; Select the explanation that correctly explains how constraints shape the feasible region and optimal choices. Associated standards listed with this skill in this prompt cell: CCSS: A-CED.3; F-IF.4 (interpret); TEKS: §111.39(c)(2)(A–J), (3)(C); VA SOL: A.EI.2 a–h; FL B.E.S.T.: MA.912.AR.2.5, 9.6; NY-NGLS: AI-A.CED.3; CA CCSSM: A-CED.3; MA 2017: HS.A-CED.3; DoDEA CCRSM; NAEP: Algebra—modeling; NCTM P2A: Practices 1, 4.. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG1.63 Interpret Intersections and Feasible Regions skill assessments:

Problem 1Difficulty: Mastery
A planned graph shows x >= 0, y >= 0, x + y <= 18, and 2x + y >= 12. Which statement best describes the feasible region?
AIt is the first-quadrant part above x + y = 18 and below 2x + y = 12.
BIt is only the line x + y = 18.
CIt contains no points because the two slanted boundaries intersect.
DIt is the first-quadrant part below x + y = 18 and on or above 2x + y = 12.
Solution & Explanation:The constraints x >= 0 and y >= 0 keep the region in the first quadrant. The <= cap is below x + y = 18, while the >= minimum is on or above 2x + y = 12.
Problem 2Difficulty: Mastery
A courier chooses x van deliveries and y bike deliveries. Constraints are x + y <= 40 and 3x + y <= 72. The boundaries intersect at (16, 24). Profit is P = 5x + 2y, and the other feasible vertices are (0, 0), (0, 40), and (24, 0). Which statement is correct?
A(0, 40) is optimal because P = 80 is greater than 128.
B(24, 0) is optimal because P = 120 is greater than 128.
C(16, 24) is optimal because P = 128 is greater than the values at the other feasible vertices.
DThe origin is optimal because it satisfies all constraints.
Solution & Explanation:The objective values are 0 at (0,0), 80 at (0,40), 120 at (24,0), and 128 at (16,24). The largest is 128.
Problem 3Difficulty: Mastery
A feasible edge is parallel to the objective lines for P = 6x + 3y, and both endpoints of that edge give P = 72. What does this imply?
AOnly one endpoint can have P = 72 because objective lines cannot be parallel to edges.
BEvery point along that feasible edge gives P = 72, so the maximum can be shared along the edge.
CThe edge cannot be part of the feasible region.
DThe objective has no value at points between endpoints.
Solution & Explanation:A linear objective changes evenly along a line. If an entire feasible edge lies on the same objective line, all points on that edge share the value.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard A-CED.3 (Primary standard selected for prompt fields in this prompt cell: CCSS A-CED.3. Skill statement in this prompt cell: Select the statement that correctly interprets intersection points, lines of intersection, and boundary lines in context; Select the explanation that correctly explains how constraints shape the feasible region and optimal choices. Associated standards listed with this skill in this prompt cell: CCSS: A-CED.3; F-IF.4 (interpret); TEKS: §111.39(c)(2)(A–J), (3)(C); VA SOL: A.EI.2 a–h; FL B.E.S.T.: MA.912.AR.2.5, 9.6; NY-NGLS: AI-A.CED.3; CA CCSSM: A-CED.3; MA 2017: HS.A-CED.3; DoDEA CCRSM; NAEP: Algebra—modeling; NCTM P2A: Practices 1, 4.. Use this prompt-provided wording as the supporting standard description for this workflow.).

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