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Grade 11 · Math · Algebra 2

11th grade Systems of inequalities with absolute value, and linear programming worksheet

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Systems of inequalities with absolute value, and linear programming

Grade 11 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Jun shades the region y ≥ 3|x + 1| + 3 and y ≤ 12. It is a triangle. What is the x-coordinate of its left top corner?

  2. Luz shades the region y ≥ 2|x − 4| + 2 and y ≤ 8. It is a triangle. What is the x-coordinate of its left top corner?

  3. Noah's bracelet plan has the corners (0, 0), (6, 0), (4, 4), (0, 7). The profit was 4x + 3y dollars. Now it is 4x + 6y dollars. What is the greatest profit?

  4. Pia's bake-sale plan has the corners (0, 0), (7, 0), (5, 3), (2, 6), (0, 6). The profit was 5x + 2y dollars. Now it is 5x + 6y dollars. What is the greatest profit?

  5. Ren's poster plan has the corners (2, 5), (4, 2), (7, 1), (9, 6). The cost was 4x + 3y dollars. Now it is 4x + 1y dollars. What is the least cost?

  6. Zee's kite plan has the corners (0, 3), (2, 0), (7, 1), (5, 7). The profit was 3x + 2y dollars. Now it is 8x + 2y dollars. What is the greatest profit?

  7. Read this first

    Flour

    2 cups per muffin tray, 5 per cookie tray, 60 cups in all. Oven: 20 trays at most. At least 4 cookie trays.

  8. Esme bakes x muffin trays and y cookie trays. The figure lists the limits. Which system fits?

    • 5x + 2y ≤ 60; x + y ≤ 20; y ≥ 4
    • 2x + 5y ≤ 60; x + y ≤ 20; x ≥ 4
    • 2x + 5y ≤ 60; x + y ≤ 20; y ≤ 4
    • 2x + 5y ≤ 60; x + y ≤ 20; y ≥ 4

  9. Time

    2 hours per poster, 3 per banner, 36 hours in all. Paper: 1 sheet per poster, 4 per banner, 40 sheets in all. At least 3 posters.

  10. Jun makes x posters and y banners. The figure lists the limits. Which system fits?

    • 2x + 3y ≤ 36; x + 4y ≤ 40; x ≥ 3
    • 2x + 3y ≤ 36; x + 4y ≤ 40; y ≥ 3
    • 3x + 2y ≤ 36; x + 4y ≤ 40; x ≥ 3
    • 2x + 3y ≤ 36; x + 4y ≤ 40; x ≤ 3

  11. Soil

    1 bag per small plant, 4 per large plant, 32 bags in all. Pots: 14 at most. At least 2 large plants.

  12. Milo sells x small and y large plants. The figure lists the limits. Which system fits?

    • 4x + y ≤ 32; x + y ≤ 14; y ≥ 2
    • 1x + 4y ≤ 32; x + y ≤ 14; y ≤ 2
    • 1x + 4y ≤ 32; x + y ≤ 14; y ≥ 2
    • 1x + 4y ≤ 32; x + y ≤ 14; x ≥ 2

  13. 3 meters per kite, 1 per pinwheel, 30 meters in all. Items: 16 at most. At least 5 pinwheels. Noah makes x kites and y pinwheels. The figure lists the limits. Which system fits?

    • 3x + y ≤ 30; x + y ≤ 16; y ≤ 5
    • 3x + y ≤ 30; x + y ≤ 16; x ≥ 5
    • x + 3y ≤ 30; x + y ≤ 16; y ≥ 5
    • 3x + y ≤ 30; x + y ≤ 16; y ≥ 5
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11th grade Systems of inequalities with absolute value, and linear programming worksheet – printable
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About this worksheet

Systems of inequalities with absolute value, and linear programming. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can tell whether a point is in a region bounded by a V and a line, and see why a strict boundary is left out.
  • I can write the limits of a story as a system and find every corner of the allowed region, including where two limits cross.
  • I can test every corner to find the best profit or least cost, and redo it when a price changes.

Standard: A-REI.D.12, A-CED.A.3

Words to know

region: All the points that pass every inequality.

corner: A point where two boundary lines meet.

constraint: A limit from the story, written as an inequality.

objective: The rule to make as big or as small as possible, like P = 4x + 3y.

Common mistakes

Checked a point in the first inequality only. A point must pass every inequality, so test it in each one together.

Checked a point in the second inequality only. A point must pass every inequality, so test it in each one together.

Counted a point on the boundary of a strict inequality (< or >). A strict inequality leaves its boundary out.

Questions parents ask

What is the most common mistake with systems of inequalities with absolute value, and linear programming?

Checked a point in the first inequality only. A point must pass every inequality, so test it in each one together.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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