Systems of inequalities with absolute value, and linear programming

Answer Key - Grade 11 Math Worksheet - Challenge Me

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. 1.

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

   63

3. Limits

   x ≥ 0; y ≥ 0; 3x + y ≤ 30; x + y ≤ 12; x + 2y ≤ 20.

4. 2.

   Pia graphs the limits in the figure. What is the greatest value of P = 4x + 5y in that region?

   56

5. Limits

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

6. 3.

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

   37

7. Limits

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

8. 4.

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

   70
9. 5.

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

   20
10. 6.

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

    10
11. 7.

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

    10

12. 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.

13. 8.

    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?

    59

14. 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.

15. 9.

    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?

    50

16. Plan

    x kites and y pinwheels. Earnings: $4 per kite, $3 per pinwheel. Items: 1 per kite, 1 per pinwheel, 12 in all. String (meters): 3 per kite, 1 per pinwheel, 18 in all. Time (hours): 4 per kite, 2 per pinwheel, 28 in all.

17. 10.

    Zee's class makes x kites and y pinwheels. The figure gives the limits. What is the most it can earn, in dollars?

    38