Additional Materials

Content Standard Strand

MATH: Algebra/Expressions & Equations

Materials Required

Estimated Time Needed

(Times are approximate and will depend on the needs of the students.)

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Optimization Problems: Boomerangs
Next Lesson/
Homework
  • Review Individual Solutions to the Assessment Task (10 minutes)
      • Ask students to read through their original responses to the assessment task.
        • Read through your original solution, and think about your work in this lesson.
        • Write down what you have learned during the lesson.
        • Which method would you prefer to use if you were doing the task again? Why?
      • Encourage students to compare the new approaches presented during the lesson with their original method.

  • Solutions
    • If one assumes that ten boomerangs are made, then the following table of possibilities may be made.

      The constraint on carving hours is broken when more than four large boomerangs are made.


      Number of Small Number of Large Total Number (≤10) Carving Hours (≤24) Profit Made

      10

      0

      10

      20

      80

      9

      1

      10

      21

      82

      8

      2

      10

      22

      84

      7

      3

      10

      23

      86

      6

      4

      10

      24

      88

      5

      5

      10

      25

      90


      This approach, however, does not include the possibility of making fewer than ten boomerangs. A more complete approach would be to draw a graph showing all possibilities.

      The possible combinations to be checked are the integer points within the bold region on the graph.

      The maximum profit occurs, however, when six small and four large boomerangs are made.

      This profit is $88.

      (This can be seen graphically by drawing lines of constant profit on the graph, e.g. 8x + 10y = 80. This idea may emerge in discussion.)

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