Question

a company manufactures 15-inch laptops and 17-inch laptops. it takes 3 hours to manufacture a 15-inch laptop and 5 hours to manufacture a 17-inch laptop. the company has 480 hours of manufacturing time available.

write a linear inequality to model this scenario. be sure to define your variables.

enter your inequality in standard form in the box provided.

define the variables from the situation above.

choose the correct answer from each drop-down to complete the statement.

let x represent

let y represent the number of 15-inch laptops

Explanation:

Step1: Define Variables

Let \( x \) represent the number of 17 - inch laptops, and let \( y \) represent the number of 15 - inch laptops.

Step2: Calculate Time for Each Laptop

The time to manufacture \( y \) 15 - inch laptops is \( 3y \) hours (since each 15 - inch laptop takes 3 hours). The time to manufacture \( x \) 17 - inch laptops is \( 5x \) hours (since each 17 - inch laptop takes 5 hours).

Step3: Formulate the Inequality

The total manufacturing time available is 480 hours. So the sum of the time taken to manufacture 15 - inch laptops and 17 - inch laptops should be less than or equal to 480 hours. So the linear inequality is \( 3y + 5x\leqslant480 \), which can be rewritten in standard form as \( 5x + 3y\leqslant480 \).

Answer:

The linear inequality is \( 5x + 3y\leqslant480 \), where \( x \) represents the number of 17 - inch laptops and \( y \) represents the number of 15 - inch laptops.