Representing Constraints ~ Adapted from Walch Education
Slide 3
Key Concepts When an inequality has one or more variables and
contains at least one inequality symbol (, , , or ), it is called
an algebraic inequality. Constraints are limits or restrictions on
the values that can be substituted into an equation or
inequality.
Slide 4
Many real-world situations can be modeled using an equation, an
inequality, or a system of equations or inequalities. A system is a
set of equations or inequalities with the same unknowns. The
solution set is the value or values that make each sentence in the
system a true statement.
Slide 5
Practice # 1 A school supply company produces wooden rulers and
plastic rulers. The rulers must first be made, and then painted. It
takes 20 minutes to make a wooden ruler. It takes 15 minutes to
make a plastic ruler. There is a maximum amount of 480 minutes per
day set aside for making rulers. It takes 5 minutes to paint a
wooden ruler. It takes 2 minutes to paint a plastic ruler. There is
a maximum amount of 180 minutes per day set aside for painting
rulers. Write a system of inequalities that models the making and
then painting of wooden and plastic rulers.
Slide 6
First, Lets Identify What We Know There is a maximum of 480
minutes for making rulers. It takes 20 minutes to make a wooden
ruler. It takes 15 minutes to make a plastic ruler. There is a
maximum of 180 minutes for painting rulers. It takes 5 minutes to
paint a wooden ruler. It takes 2 minutes to paint a plastic
ruler.
Slide 7
Write the inequalities The inequality representing the amount
of time to make the rulers: Let w represent the wooden rulers and p
represent the plastic rulers. 20w + 15p 480 The inequality
representing the amount of time to paint the rulers: Let w
represent the wooden rulers and p represent the plastic rulers. 20w
+ 15p 480
Slide 8
Are there Any Additional Constraints? You guessed it! It is not
possible to produce a negative amount of either wooden rulers or
plastic rulers So how do we limit the values of w and p? w 0 p
0
Slide 9
Combine all the inequalities We list all the related
inequalities in a brace, {
Slide 10
Your Turn Use the system of inequalities below to give a
possible solution to the system.