Q: A local electronic store provides customers with walk-in service to repair their flat screen TVs of various technologies (LCD, LED, Plasma, etc.). When an item arrives, store technicians perform basic tests at the test shop (station 1) and decide which rework shop to send for repair. Cleaning shop (station 2) is responsible for providing minor cosmetic repair work such as cleaning. Rework shop (station 3) provides moderate repair work such as replacing power supply unit of the panel. Due to its current limited capability, the store is not capable of fixing more serious damage and can only send customers away for some cases.
On average, flat screen set arrives the store at a rate of ten per hour. After testing at station 1, 20% of the units, which are seriously damaged and cannot be fixed, must leave the store. 50% of the units, which only need minor repair, will be sent to station 2. The remaining 30% will be sent to station 3. Usually, it takes an average of 20 minutes per unit at station 1, 10 minutes at station 2, 50 minutes at station 3. On average, 5 flat screen sets wait in front of station 1, 3 in front of station 2, and 5 in front of station 3. Assuming that the process is stable, answer the following questions:
a) On average, how long does a flat screen set stay in the shop?
b) What is the average number of flat screen sets in the store?