Systems of inequalities with absolute value, and linear programming

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Esme shades the region y ≥ 2|x − 3| − 2 and y ≤ 6. It is a triangle. What is the x-coordinate of its left top corner?

   -1
2. 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?

   1
3. 3.

   Milo shades the region y ≤ −2|x + 2| + 10 and y ≥ 2. It is a triangle. What is the x-coordinate of its left bottom corner?

   -6
4. 4.

   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?

   42
5. 5.

   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?

   46
6. 6.

   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?

   13
7. 7.

   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?

   58

8. Read this first

   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.

9. 8.

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

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

10. Soil

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

11. 9.

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

    • 1x + 4y ≤ 32; x + y ≤ 14; x ≥ 2
    • 1x + 4y ≤ 32; x + y ≤ 14; y ≥ 2
    • 1x + 4y ≤ 32; x + y ≤ 14; y ≤ 2
    • 4x + y ≤ 32; x + y ≤ 14; y ≥ 2
12. 10.

    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; x ≥ 5
    • x + 3y ≤ 30; x + y ≤ 16; y ≥ 5
    • 3x + y ≤ 30; x + y ≤ 16; y ≤ 5
    • 3x + y ≤ 30; x + y ≤ 16; y ≥ 5