a furniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa…

a furniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply. y≥2x y≤2x 10x + 20y≥300 10x + 20y≤300 done

a furniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply. y≥2x y≤2x 10x + 20y≥300 10x + 20y≤300 done

Answer

Explanation:

Step1: Analyze fabric - yardage constraint

The fabric used for chairs is 10x yards (since each chair requires 10 yards and there are x chairs) and for sofas is 20y yards (since each sofa requires 20 yards and there are y sofas). The manufacturer has 300 yards of fabric available. So the total fabric used for chairs and sofas must be less than or equal to 300 yards. The inequality for fabric - yardage is $10x + 20y\leq300$.

Step2: Analyze the relationship between number of sofas and chairs

The number of sofas must be at least twice the number of chairs. This means $y\geq2x$.

Answer:

y ≥ 2x 10x + 20y ≤ 300