Essay

Verifying Warehouse Clearance Zones Using Test Points

You are working as a junior facility designer planning overlapping safety clearance zones on a warehouse floor. The layout constraints are modeled by the system of inequalities:

  1. y3x+1y \ge 3x + 1
  2. 3x+y4-3x + y \ge -4

To ensure your coordinates are mapped correctly, your team supervisor asks you to explain how to verify if the warehouse's primary supply hub, located at the origin (0, 0), falls within the allowed region for each constraint.

Write a short essay recalling the standard mathematical procedure for using a test point to determine the correct shaded region. Your explanation must include:

  1. A description of the step-by-step process of using a test point (like the origin) to decide which side of a boundary line to shade.
  2. The specific simplified numerical statements obtained when you substitute the test point (0, 0) into both inequalities.
  3. A clear statement of whether each inequality evaluates to true or false at this point, and recall what this indicates about whether the origin is included in the shaded region for each individual inequality.

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Updated 2026-06-17

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