Evanston Inc. manufactures gas-fired heaters together with circulator pumps and motors. The entire unit circulates hot water through baseboards in the house. The company recently developed a compact unit, Model 390Z, that replaces the circulator pump and motor. The unit requires little maintenance and is warranted to operate trouble free for 3 years. The company has established a reputation for high-quality products, and the company's management forecasts an annual demand of 1,000,000 units of Model 390Z.
The bill of materials for a unit of Model 390Z requires one precision ball bearing. The diameter of the bearing is 2.75 centimeters, and the engineering specifications do not allow tolerances beyond plus or minus 5%. If the actual bearing size is greater than the specification, the bearing will not fit in the casing. If the bearing is smaller than the specification, the unit will not function efficiently. The bearings used in the Model 390Z are not subjected to quality control inspection prior to assembly of the unit; however, the entire unit is performance tested after final assembly. Based on the pilot production runs, the following information has been gathered.
(a) Cost for a unit of Model 390Z:

(b) The majority of the rejections experienced during the pilot run were related to the ball bearings.
(c) During assembly, bearings that are too big to fit in the casing are rejected, and new bearings are used. This change in bearings requires 6 minutes of additional direct labor for each affected unit.
(d) Units rejected during performance testing are reassembled with a new bearing. On average, one additional hour of labor is required for reassembly.
(e) The defective bearings are returned to the supplier for credit.
J. McGill, the company production manager, collected additional data on the rejections during the pilot production runs. McGill's estimate of the probability of rejections for a lot of 1,000 bearings is as follows:

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Material (including the bearing at $5). Labor (5 hours at $8 per hour). Variable overhead (150% of labor cost) $ 30 40 60 $130 e cost.