Interpreting Constraints and Units

Learn outlier fences, checking constraints and units.

Lesson 3 of 32 parts Practice Flashcards

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Outlier Fences

Objective: Explain outlier fences, apply the stated method, and check its conditions.

The conventional 1.5·IQR rule flags observations below Q1−1.5IQR or above Q3+1.5IQR. A flag is a prompt for investigation, not evidence of error. Retain unusual valid observations unless a justified analysis decision calls for different handling. A flagged outlier is not automatically an invalid observation.

Formulas

$Lower=Q1−1.5IQR; upper=Q3+1.5IQR$

Worked examples

Try itA rectangle against a wall uses 28 m of fence on three sides. Its two perpendicular sides are x. Find the x maximizing area.Show answer

Step 1: The parallel fenced side is 28−2x. Step 2: A=x(28−2x), so A′=28−4x=0. Step 3: x=7 m; the other dimension is 14 m.

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Outlier Fences

Objective: Explain outlier fences, apply the stated method, and check its conditions.

Formulas

$Lower=Q1−1.5IQR; upper=Q3+1.5IQR$

Worked examples

Try itA rectangle against a wall uses 28 m of fence on three sides. Its two perpendicular sides are x. Find the x maximizing area.Show answer

Step 1: The parallel fenced side is 28−2x. Step 2: A=x(28−2x), so A′=28−4x=0. Step 3: x=7 m; the other dimension is 14 m.

Checking Constraints and Units

Objective: Explain checking constraints and units, apply the stated method, and check its conditions.

A computed optimum must satisfy the original resource equation and positivity restrictions. Objective units follow the modeled quantity: area uses square length, while a side length uses length. Reconstructing the design checks both feasibility and interpretation. A feasible design and its objective value use different units.

Formulas

Resource check: 2x+y=F

Worked examples

Try itA rectangle against a wall uses 28 m of fence on three sides. Find its maximum area.Show answer

Step 1: The optimum perpendicular side is 7 m. Step 2: The remaining fenced side is 28−2(7)=14 m. Step 3: The area is 98 m², not meters.

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