DECISION MAKING

 

GOALS

1.      Plot points and draw graphs of straight lines.

2.      Understand the concept of fair exchange (in terms of both the context and the graph).

3.      Understand the concept of constraint (in terms of both the context and the graph).

4.      Understand and know how to find feasible and unfeasible regions.

5.      Understand and use the inequality symbols  ≤, ≥, <, and >.

6.      Find the value of a given combination of items and find a combination for a given value.

7.      Understand that all of the solutions to a linear equation lie on a line.

8.      Use tables and charts to systematically organize information.

9.      Identify the constraints in a given problem situation.

10.  Use fair exchange as a way to draw graphs and to find new combinations.

11.  Understand and use the relationships among constraints , dividing lines, and feasible and unfeasible regions.

12.  Interpret and organize information presented in a story in mathematical terms.

13.  Combine different kinds of information (multiple constraints) in one graph and make decisions based on the information.

14.  Solve a complex problem using a mathematical model, and translate the solution back in terms of the context.

15.  Recognize that mathematics can be used to describe and clarify complex situations.

 

SECTION SUMMARIES

 

SECTION A:  Feasible Plans

1.       Coordinates on a graph can be used to represent plans.  For example the point (5,8) can represent 5 houses and 8 town houses.

2.       When selecting a plan that works, it helps to consider the boundaries and to determine which plans are feasible and which are unfeasible.

 

SECTION B:  Fair Exchange

1.       If you have one plan you know is feasible and you take away something you must gain something else to compensate.  This is called fair exchange.  For example, losing 2 houses at 600 m2 each is balanced out by gaining 3 town houses at 400 m2 each.  Both are worth a total of 1200 m2.

2.       In this section you discovered some important facts:  All plans that use the same area lie on a line; fair exchange can be used to find all plans that use the same area; and a dividing line splits plans into those that are feasible and those that are unfeasible.

 

SECTION C:   More Exchanging

      1.    This section showed that what you learned about graphing and fair exchange in preceding section can be

applied to many different situations.

      2.    A constraint, such as the amount of land available, can change.  When the constraint changes, the dividing

line moves but is still parallel to the first line.

       

SECTION D:   More Constraints

1.    In real situations there is usually more than one constraint.  Each constraint splits a diagram into two regions.  Then a second constraint can continue splitting regions into smaller and smaller feasible regions.

2.    In this section, the feasible region became smaller and smaller as we added constraints.  Sometimes, however, constraints can be changed to allow for more possibilities.