Let's break down the problem step by step to identify the inequalities that describe it.
1. Twice as many sofas as chairs:
- We are told that the manufacturer must produce at least twice as many sofas (\(y\)) as chairs (\(x\)).
- This can be expressed as the inequality \(y \geq 2x\).
2. Fabric constraints:
- Each chair requires 10 yards of fabric.
- Each sofa requires 20 yards of fabric.
- The total amount of fabric available is 300 yards.
- This can be expressed as \(10x + 20y \leq 300\).
To summarize, the inequalities that describe the given problem are:
- \(y \geq 2x\)
- \(10x + 20y \leq 300\)
So, we check these boxes:
- \(y \geq 2x\)
- \(10x + 20y \leq 300\)
The inequalities [tex]\(y \leq 2x\)[/tex] and [tex]\(10x + 20y \geq 300\)[/tex] do not correctly describe the constraints given in the problem.
