2. Representing Constraints ~ Adapted from Walch Education

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.

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.

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.

6. First, Let’s 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.

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

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

9. Combine all the inequalities We list all the related inequalities in a brace, {

10. Your Turn… Use the system of inequalities below to give a possible solution to the system.

11. Thanks for Watching!!! ~ Dr. Dambreville