Bottled water and medical supplies are to be shipped to...

Bottled water and medical supplies are to be shipped to survivors of a hurricane by plane. Each plane can carry a total volume that does not exceed 6000 cubic feet. Each water bottle is 2 cubic feet and each medical kit has a volume of 1 cubic foot. Let $x$ represent the number of bottles of water to be shipped. Let $y$ represent the number of medical kits. The plane's volume limitations can be described by the following inequality: (FIGURE CAN'T COPY) a. Graph the inequality. Because $x$ and $y$ must be nonnegative, limit the graph to quadrant I and its boundary only. b. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?

Bottled water and medical supplies are to be shipped to survivors of a hurricane by plane. Each plane can carry a total volume that does not exceed 6000 cubic feet. Each water bottle is 2 cubic feet and each medical kit has a volume of 1 cubic foot. Let $x$ represent the number of bottles of water to be shipped. Let $y$ represent the number of medical kits. The plane's volume limitations can be described by the following inequality:
(FIGURE CAN'T COPY)
a. Graph the inequality. Because $x$ and $y$ must be nonnegative, limit the graph to quadrant I and its boundary only.
b. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?

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Key Concepts

Linear Inequality

A linear inequality, such as 2x + y ? 6000, represents a constraint where combinations of x and y values must satisfy the condition that they do not exceed a certain limit. This type of inequality is used to model real-world limitations, such as capacity restrictions in shipping scenarios, and forms the basis for defining the relationships between different quantities.

Feasible Region

The feasible region consists of all points (x, y) that satisfy the given constraints, including the inequality 2x + y ? 6000 and the non-negativity conditions (x ? 0 and y ? 0). This region, when graphed, represents all acceptable solutions to the problem, ensuring that the physical restrictions, like volume capacity, are not exceeded.

Graphing Constraints in the First Quadrant

Graphing the inequality in the first quadrant involves plotting the boundary line—obtained by setting the inequality as an equality—and then shading the area corresponding to all solutions that meet the inequality condition. Due to the non-negativity constraints on x and y, only the part of the graph in the first quadrant is considered, illustrating the practical limits of the problem context.