Furniture Sales. A distributor wholesales desk chairs for...

Furniture Sales. A distributor wholesales desk chairs for $$150$ and side chairs for $100 .$ Best Furniture wants to order no more than $900$ worth of chairs, including more side chairs than desk chairs, from that distributor. Use the illustration to graph a system of inequalities that will show the possible combinations of the number of desk chairs $(x)$ and the number of side chairs ( $y$ ) that can be ordered. Give two possible solutions. ( GRAPH CANNOT COPY)

Key Concepts

Linear Inequalities

Linear inequalities represent relationships with a linear expression where one side is constrained to be less than or equal to, or greater than or equal to, a constant or another linear expression. In problems like this, they serve to model real-world limitations such as budget constraints or quantity requirements.

System of Inequalities

A system of inequalities consists of multiple linear inequalities that are considered together. The solution to the system is the set of all points that simultaneously satisfy every inequality, which is essential for modeling problems where multiple constraints, such as budget and relative quantity restrictions, must be met.

Feasible Region

The feasible region is the area on a graph where all the inequalities in a system overlap. This region represents all possible combinations of decision variables that satisfy every constraint in the problem. In the context of ordering chairs, it includes every combination of desk and side chairs that meets both the cost limitation and the condition of ordering more side chairs than desk chairs.

Graphical Representation of Constraints

Graphing the constraints by plotting each inequality on a coordinate plane allows visualization of the feasible region. This method helps in understanding how different constraints interact and where optimal solutions or acceptable combinations lie, such as identifying specific combinations of quantities that fulfill all conditions at once.

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