Monitoring Air Quality in a Warehouse

You work as a safety coordinator at a large distribution warehouse. Air quality sensors throughout the building measure particulate concentration, which varies based on location due to ventilation patterns and equipment placement. Understanding how concentration levels change across the warehouse floor—and eventually throughout the full three-dimensional space—helps you determine where to install additional filtration units and place warning signage. The particulate concentration (measured in micrograms per cubic meter above the acceptable baseline) at any point on the warehouse floor is modeled by [latex]P(x, y) = 18 - 2x^2 - 2y^2[/latex], where [latex]x[/latex] and [latex]y[/latex] are measured in tens of meters from the center of the building.