Question

A company is producing two types of headphones, A and B. The production process for both types require two different components, X and Y, that are outsourced. Headphone type A requires 3 units of component × and 5 units of component Y, while headphone type B requires 4 units of component X and 2 units of component Y. The defect rates for the components are: dX = 0.04 and dY = 0.02. The company needs to produce 20,000 units of headphone type A and 30,000 units of headphone type B. Determine the initial requirements for each component to meet the demand.

Answer 1

To determine the initial requirements for each component to meet the demand, we can use a system of equations. Let's denote the number of units of component X required for headphones A and B as XA and XB respectively, and the number of units of component Y required for headphones A and B as YA and YB respectively.

Step-by-step explanation:

To determine the initial requirements for each component to meet the demand, we can use a system of equations. Let's denote the number of units of component X required for headphones A and B as XA and XB respectively, and the number of units of component Y required for headphones A and B as YA and YB respectively.

We know that headphone type A requires 3 units of component X and 5 units of component Y, and headphone type B requires 4 units of component X and 2 units of component Y. We also know that the company needs to produce 20,000 units of headphone type A and 30,000 units of headphone type B.

So we can set up the following equations:

XA + XB = 20,000 (equation 1)

YA + YB = 30,000 (equation 2)

3XA + 4XB = total units of component X (equation 3)

5YA + 2YB = total units of component Y (equation 4)

To solve the system of equations, we can first solve equations 1 and 2 to find the values of XA and XB, and YA and YB. Then we can substitute these values into equations 3 and 4 to find the total units of component X and component Y required.