PencilGo

Grade 11 · Math · Algebra 2

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

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version
Print

Systems of inequalities with absolute value, and linear programming

Grade 11 Math Worksheet - Challenge Me

NameDate

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

  1. Read this first

    Limits

    x ≥ 0; y ≥ 0; x + 2y ≤ 16; x + y ≤ 12; 2x + 3y ≤ 27.

  2. Noah graphs the limits in the figure. What is the greatest value of P = 5x + 6y in that region?

  3. Limits

    x ≥ 0; y ≥ 0; x + 2y ≤ 22; x + y ≤ 15; 2x + y ≤ 26.

  4. Ren graphs the limits in the figure. What is the greatest value of P = 2x + 3y in that region?

  5. Limits

    x ≥ 0; y ≥ 0; x + 3y ≤ 21; x + y ≤ 11; x + 2y ≤ 15.

  6. Zee graphs the limits in the figure. What is the greatest value of P = 6x + 7y in that region?

  7. Esme graphs the region y ≥ |x − 3| + 1, y ≤ 8 and x ≤ 6. What is the greatest value of P = 4x − y there?

  8. Jun graphs the region y ≥ |x − 2| + 2, y ≤ 9 and x ≤ 5. What is the greatest value of P = 3x − y there?

  9. Luz graphs the region y ≥ |x + 1| + 0, y ≤ 6 and x ≤ 4. What is the greatest value of P = 5x − 2y there?

  10. Milo graphs the region y ≥ |x + 2| + 1, y ≤ 7 and x ≥ −3. What is the greatest value of P = −4x − y there?

  11. Plan

    x muffin trays and y cookie trays. Earnings: $7 per muffin tray, $5 per cookie tray. Oven (trays): 1 per muffin tray, 1 per cookie tray, 11 in all. Flour (cups): 2 per muffin tray, 1 per cookie tray, 14 in all. Time (hours): 3 per muffin tray, 2 per cookie tray, 24 in all.

  12. Noah's bake sale makes x muffin trays and y cookie trays. The figure gives the limits. What is the most it can earn, in dollars?

  13. Plan

    x bird feeders and y planters. Earnings: $5 per bird feeder, $7 per planter. Wood (boards): 2 per bird feeder, 2 per planter, 26 in all. Time (hours): 2 per bird feeder, 1 per planter, 22 in all. Paint (cans): 1 per bird feeder, 2 per planter, 20 in all.

  14. Pia's club makes x bird feeders and y planters. The figure gives the limits. What is the most it can earn, in dollars?

  15. Plan

    x large posters and y small posters. Earnings: $4 per large poster, $5 per small poster. Card (sheets): 1 per large poster, 3 per small poster, 18 in all. Ink (bottles): 2 per large poster, 4 per small poster, 28 in all. Time (hours): 2 per large poster, 2 per small poster, 24 in all.

  16. Ren's team makes x large posters and y small posters. The figure gives the limits. What is the most it can earn, in dollars?

PencilGopencilgo.com

11th grade Systems of inequalities with absolute value, and linear programming worksheet – printable
Print: 123456

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.

More algebra 2

See all Algebra 2

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records

Ready for easier practice?

Print a sheet, scan it when it’s done, and PencilGo picks the next one.

Create a free account