Calculating Material Needs for a Shelter Floor

You are volunteering with a disaster relief organization that builds temporary shelters. Your task is to calculate the amount of insulating foam needed for the floor of a new shelter. The shelter floor is rectangular, measuring [latex]5[/latex] meters by [latex]4[/latex] meters. Due to the uneven ground beneath, the foam thickness varies across the floor according to the function [latex]f(x,y) = 6 - x - y[/latex] centimeters, where [latex]x[/latex] is the distance in meters from the west edge and [latex]y[/latex] is the distance in meters from the south edge. To determine the total volume of foam required, you need to evaluate a double integral over this region. Later, you’ll also help calculate materials for a triangular storage area where the integration region is not rectangular.