4. 4.1. A firm manufactures self-assembling furniture for iFurniture. The manufacturer aims to reduce the cost of returned orders (i.e., the external cost of quality) through better quality management practices. To that end, the manager of the quality control department inspects the final packages each day using randomly selected samples. The defects include wrong parts, missing connection parts, parts with apparent painting problems, and parts with rough surfaces. The average defect rate is four per day. 4.1.1. What type of control chart should be used? Why? 4.1.2.Calculate three-sigma lower and upper control limits. Construct a control chart with three- sigma control limits. Explain why the lower control limit cannot be less than zero. Today the manager discovered 12 defects. What does this mean? Why? 4.2. Suppose, now, the manufacturer is attempting to develop a quality monitoring system for some parts purchased from its supplier. These parts are either good or defective. The manager has decided to take a sample of 200 units. The defect rate has historically been about 3.5%. 4.2.1. What type of control chart should be used? Why? 4.2.2. What are the upper and lower control limits if the manager wishes to use three-sigma limits? Today the manager discovered fourteen defects. What does this mean? Why?