Representing Constraints

Representing Constraints~ Adapted from Walch Education

Key ConceptsWhen 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.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.

Practice # 1A 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.

First, Lets Identify What We KnowThere 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.

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

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 0p 0

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

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

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