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Representing Constraints ~ Adapted from Walch Education

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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.

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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.

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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.

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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.

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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

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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

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

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

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Thanks for Watching!!! ~ Dr. Dambreville