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ALG2.62 Sensitivity and Constraint Reasonableness Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.62 Sensitivity and Constraint Reasonableness. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.62 Sensitivity and Constraint Reasonableness - Select the statement that best describes how changing a constraint changes the feasible region and potentially the optimal solution in an optimization problem. Associated source-listed standards: CCSS ★ Modeling; MP.4; CA CCSSM ★ Modeling; MP.4; MA 2017 ★ Modeling; MP.4; NY NGLS ★ Modeling; MP.4; TX TEKS Algebra II: §111.40.

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 II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related ALG2.62 Sensitivity and Constraint Reasonableness skill assessments:

Problem 1Difficulty: Mastery

For R = 3x + 10y, the current corner-point values are (0, 0) -> 0; (10, 0) -> 30; (8, 4) -> 64; (0, 8) -> 80. The constraint 2x + y <= 20 is relaxed to 2x + y <= 23. What is the new maximum value of the objective function?

Solution & Explanation:After applying the change and checking the new corner points, the maximum is 80 at (0, 8).

Problem 2Difficulty: Mastery

In a water-testing schedule, x represents site A tests and y represents site B tests. Minimize E = 9x + 9y subject to x >= 0; y >= 0; x <= 13; y <= 12; 2x + y >= 11; x + 2y >= 7. At the original optimal point (5, 1), the constraint x + 2y >= 7 is binding. The model changes x + 2y >= 7 to x + 2y >= 5. What is the best conclusion after the change?

AThe feasible region expands, but the minimum stays 54 at (5, 1).

BMore points become feasible, and the minimum changes to 49.5 at (5.5, 0).

CFewer points remain feasible, and the minimum changes to 49.5 at (5.5, 0).

DThe model becomes infeasible, so no minimum exists.

Solution & Explanation:Because x + 2y >= 7 is binding at (5, 1), changing it directly affects the boundary that contains the old optimum. The change keeps every old feasible point and adds new ones. One of the added possibilities gives a lower value, so the minimum becomes 49.5 at (5.5, 0).

Problem 3Difficulty: Mastery

For M = 9x + 4y, the current corner-point values are (0, 0) -> 0; (13, 0) -> 117; (13, 7) -> 145; (8, 12) -> 120; (0, 12) -> 48. Revision A: The model changes x + y <= 20 to x + y <= 21. Revision B: A new constraint x + y >= 21 is added. The model is changed in two different ways. Which comparison is accurate?

AUnder Revision A, the feasible region expands, and the maximum becomes 149 at (13, 8); under Revision B, the model becomes infeasible, so no maximum exists.

BUnder Revision A, the feasible region expands, and the maximum becomes 149 at (13, 8); under Revision B, the feasible set becomes larger, so the maximum stays 145 at (13, 7).

CUnder Revision A, the model becomes infeasible, so no maximum exists; under Revision B, the feasible region expands, and the maximum becomes 149 at (13, 8).

DUnder Revision A, the feasible region shrinks, so the maximum stays 145 at (13, 7); under Revision B, the model becomes infeasible, so no maximum exists.

Solution & Explanation:Analyze each revision separately. Under Revision A, the feasible region expands, and the maximum becomes 149 at (13, 8). Under Revision B, the model becomes infeasible, so no maximum exists.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard ★ Modeling (Select the statement that best describes how changing a constraint changes the feasible region and potentially the optimal solution in an optimization problem. Associated source-listed standards: CCSS ★ Modeling; MP.4; CA CCSSM ★ Modeling; MP.4; MA 2017 ★ Modeling; MP.4; NY NGLS ★ Modeling; MP.4; TX TEKS Algebra II: §111.40.).