SECONDARY MATH I // MODULE 5

SYSTEMS OF EQUATIONS AND INEQUALITIES – 5.5

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5. 5 All For One, One For All

A Solidify Understanding Task

CarlosandClaritahavefoundawaytorepresentcombinationsofcatsanddogsthatsatisfy

eachoftheirindividual“PetSitter”constraints,buttheyrealizethattheyneedtofindcombinations

thatsatisfyalloftheconstraintssimultaneously.Why?

1. Beginbylistingthesystemofinequalitiesyouhavewrittentorepresentthestart-upcosts

andspace“PetSitter”constraints.

2. Findatleast5combinationsofcatsanddogsthatwouldsatisfybothoftheconstraintsrepresentedbythissystemofinequalities.Howdoyouknowthesecombinationswork?

3. Findatleast5combinationsofcatsanddogsthatwouldsatisfyoneoftheconstraints,butnottheother.Foreachcombination,explainhowyouknowitworksforoneoftheinequalities,butnotfortheother?

4. Shadearegiononthecoordinategridthatwouldrepresentthesolutionsettothesystemofinequalities.Explainhowyoufoundtheregiontoshade.

5. Rewriteyoursystemsofinequalitiestoincludetheadditionalconstraintsforfeedingtimeandpamperingtime.

6. Findatleast5combinationsofcatsanddogsthatwouldsatisfyalloftheconstraintsrepresentedbythisnewsystemofinequalities.Howdoyouknowthesecombinationswork?

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SECONDARY MATH I // MODULE 5

SYSTEMS OF EQUATIONS AND INEQUALITIES – 5.5

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

7. Findatleast5combinationsofcatsanddogsthatwouldsatisfysomeoftheconstraints,butnotallofthem.Foreachcombination,explainhowyouknowitworksforsomeinequalities,butnotforothers?

8. Shadearegionofthecoordinategridthatwouldrepresentthesolutionsettothesystemofinequalitiesconsistingofall4“PetSitter”constraints.Explainhowyoufoundtheregiontoshade.

9. Shadearegioninquadrant1ofthecoordinategridthatwouldrepresentallpossiblecombinationsofcatsanddogsthatsatisfythe4“PetSitter”constraints.ThissetofpointsisreferredtoasthefeasibleregionsinceCarlosandClaritacanfeasiblyboardanyofthecombinationsofcatsanddogsrepresentedbythepointsinthisregionwithoutexceedinganyoftheirconstraintsontime,moneyorspace.

10. Howisthefeasibleregionshadedin#9differentfromthesolutionsettothesystemofinequalitiesshadedin#8?

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