Questions: A company produces foam mattresses in two sizes: regular and king size. It takes 2 minutes to cut the foam for a regular mattress and 6 minutes for a king mattress. If the cutting department has 20 labor-hours available each day, how many regular and king mattresses can be cut in one day? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph. Let x be the number of regular mattresses cut per day and let y be the number of king mattresses cut per day. Choose the correct inequality with appropriate non-negative restrictions below. A. 6x + 2y ≥ 1200, x ≥ 0, y ≥ 0 B. 2x + 6y ≤ 20, x ≥ 0, y ≥ 0 C. 2x + 6y ≤ 1200, x ≥ 0, y ≥ 0 D. 6x + 2y ≥ 20, x ≥ 0, y ≥ 0

A company produces foam mattresses in two sizes: regular and king size. It takes 2 minutes to cut the foam for a regular mattress and 6 minutes for a king mattress. If the cutting department has 20 labor-hours available each day, how many regular and king mattresses can be cut in one day? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph.

Let x be the number of regular mattresses cut per day and let y be the number of king mattresses cut per day. Choose the correct inequality with appropriate non-negative restrictions below.
A. 6x + 2y ≥ 1200, x ≥ 0, y ≥ 0
B. 2x + 6y ≤ 20, x ≥ 0, y ≥ 0
C. 2x + 6y ≤ 1200, x ≥ 0, y ≥ 0
D. 6x + 2y ≥ 20, x ≥ 0, y ≥ 0

Transcript text: A company produces foam mattresses in two sizes: regular and king size. It takes 2 minutes to cut the foam for a regular mattress and 6 minutes for a king mattress. If the cutting department has 20 labor-hours available each day, how many regular and king mattresses can be cut in one day? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph. Let $x$ be the number of regular mattresses cut per day and let $y$ be the number of king mattresses cut per day. Choose the correct inequality with appropriate non-negative restrictions below. A. $6 x+2 y \geq 1200, x \geq 0, y \geq 0$ B. $2 x+6 y \leq 20, x \geq 0, y \geq 0$ C. $2 x+6 y \leq 1200, x \geq 0, y \geq 0$ D. $6 x+2 y \geq 20, x \geq 0, y \geq 0$

Solution

Solution Steps

Step 1: Convert labor-hours to minutes

The problem states that the cutting department has 20 labor-hours available each day. Since there are 60 minutes in an hour, the total available time in minutes is $20 \text{ hours} \times 60 \frac{\text{minutes}}{\text{hour}} = 1200 \text{ minutes}$.

Step 2: Set up the inequality

It takes 2 minutes to cut the foam for a regular mattress and 6 minutes for a king mattress. Let $x$ represent the number of regular mattresses and $y$ represent the number of king mattresses. The total time spent cutting the foam for regular and king mattresses must be less than or equal to the total available time, which is 1200 minutes. Therefore, the inequality is $2x + 6y \le 1200$.

Step 3: Non-negative restrictions

The number of mattresses cannot be negative, so we must include the non-negative restrictions: $x \ge 0$ and $y \ge 0$.