GET THE MOST OUT OF
IT
GOALS
1.
understand
and graph equations of the form AX + BY = C
2.
find
a common solution to a pair of equations algebraically and graphically
3.
understand
and graph inequalities to form a feasible region
4.
understand
and graph hyperbolas of the form XY = K
5.
understand
how changing positions of the rolling line affect values of the objective
function
6.
use
the rolling line in different optimization situations
7.
understand
and use the relationship between equations, inequalities, and graphs
8.
interpret
and organize information presented in a story in mathematical terms (using
equations, inequalities, and graphs)
9.
appreciate
and understand the power of algebra for representing and solving problems
10.
model
situations using algebra to solve simple linear programming problems
1. To solve
shopping equations, you used both a table (notebook notation) and equations.
2.
The
equation 2X + 5Y = 100 has two unknowns, so it has many solutions. When a pair of values satisfies two such
equations with two unknowns, that pair of values it called a common solution.
1.
To find the common solution you can use three different methods: graph the two equations and determine the
intersection point; make a table
for both equations and find the combination that is in both tables; and solve
the
equations as if they were shopping
equations.
2.
Fair
Exchange Principle: trading between the
two unknowns without changing the total amount needed for the combination.
SECTION C: GRAPHING CONSTRAINTS
1.
To
solve a problem, you first write equations and inequalities.
2.
To
graph a feasible region: draw the
borderline(s); decide which side of the borderline contains “favorable” points;
then shade the feasible region.
3.
Some
feasible regions have borders that are curves rather than straight lines.
SECTION D: THE ROLLING LINE
1. To find a program that uses the maximum or minimum amount of
energy within a feasible region, you used a
rolling energy
line. You looked at energy values for
points on the line and in the feasible region.
1.
In
this section you solved optimization problems.
In an optimization problem, you select from values for two or more
unknowns to maximize or minimize some other value.
1. In this section, you investigated a curve
called a hyperbola. You put all the
rectangles with a fixed perimeter
on
the coordinate axes, and saw that their upper-right vertices lie on a
line. Using all the rectangles with a
fixed
area, you saw that the upper-right vertices lie on a hyperbola.