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Representing Constraints

Representing Constraints. ~ Adapted from Walch Education. Key Concepts. When an inequality has one or more variables and contains at least one inequality symbol (<, >, ≤, ≥, or ≠), it is called an algebraic inequality .

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Representing Constraints

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  1. Representing Constraints ~ Adapted from Walch Education

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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

  7. 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

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

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

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

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