The Factory Production Line
A factory produces widgets on two assembly lines, Line A and Line B. Line A produces 200 widgets per hour, and Line B produces 150 widgets per hour. Both lines operate 8 hours a day, 5 days a week. The factory has a quality control (QC) station that inspects every widget. The QC station can inspect 300 widgets per hour and operates only during the same hours as the lines. However, the QC station requires a 15-minute break every 2 hours. Additionally, 5% of widgets from Line A and 3% from Line B are defective and must be reworked. Rework takes 10 minutes per defective widget and is done by a separate team that works only 6 hours a day. The factory manager wants to know if the QC station can keep up with production, and whether the rework team can handle the defective widgets.
1. Calculate the total number of widgets produced per day by both lines, and the total number of defective widgets per day.
Read the worked answer
Line A: 200 widgets/hour × 8 hours = 1600 widgets/day. Line B: 150 widgets/hour × 8 hours = 1200 widgets/day. Total production = 1600 + 1200 = 2800 widgets/day. Defective from A: 5% of 1600 = 0.05 × 1600 = 80 widgets. Defective from B: 3% of 1200 = 0.03 × 1200 = 36 widgets. Total defective = 80 + 36 = 116 widgets/day.
2. Determine the QC station's available inspection time per day and whether it can inspect all widgets produced. Show your reasoning.
Read the worked answer
QC operates 8 hours/day, but takes a 15-minute break every 2 hours. In an 8-hour shift, there are 8/2 = 4 two-hour blocks. After each 2-hour block, a 15-minute break is taken, but typically the break after the last block might not occur if the shift ends. Assuming breaks after the first 3 blocks (since after 8 hours the shift ends), total break time = 3 × 15 = 45 minutes = 0.75 hours. So available inspection time = 8 - 0.75 = 7.25 hours. Inspection capacity = 300 widgets/hour × 7.25 hours = 2175 widgets. Total production = 2800 widgets, which exceeds capacity by 2800 - 2175 = 625 widgets. Therefore, the QC station cannot inspect all widgets; it falls short by 625 widgets per day.
3. Calculate the total rework time required per day and determine if the rework team can handle it within their 6-hour workday.
Read the worked answer
Total defective widgets = 116 per day. Rework time per widget = 10 minutes. Total rework time = 116 × 10 = 1160 minutes = 19.33 hours. Rework team works 6 hours/day = 360 minutes. Required time (1160 minutes) far exceeds available time (360 minutes). The team can only rework 360/10 = 36 widgets per day. So they cannot handle all defective widgets; they fall short by 116 - 36 = 80 widgets per day.