The Elon Company manufactures parts for an aircraft company using three computerized numerical controlled (CNC) turning centers. The company wants to decide which machines are capable of producing a specific part with design specifications of 0.0960 inches ±0.018 inches. The machines have the following process parameters: Machine 1: X= 0.1095, σ = 0.0004 Machine 2: X = 0.0912, σ = 0.006 Machine 3: X = 0.0992, σ = 0.003 Determine which machines (if any) are capable of producing the products within the design specifications.

The mean service time (x¯) of a hairdresser is 18 minutes with a standard deviation (σ) of 2 minutes. Upper specification limit (USL) is 22 minutes, whereas lower specification limit (LSL) is 15 minutes for this process. What is the process capability index (cpk) for this process? Is the process capable?   Cpk=0.67, capable Cpk=1.5, capable Cpk=0.67, not capable Cpk=0.5, capable Cpk=0.5, not capable

STAR Co. provides paper to smaller companies with volumes that are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established. 12-ft 15-ft 30-ft Trim Loss (ft) Min s.t. 12-f Pattern Number 15-1 1 30-1 2 3 4 5 0 D 8 3 7 6 0 0 0 1 0 3 0 2 0 10 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12)+ 0(15) + 2(30) 96 feet used results in 100-96-4 foot of trim loss). Orders in hand for the coming week are 5,660 12- foot rolls, 1,690 15-foot rolls, and 3,340 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held. 10 (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five…

Bottles for room spray are supposed to weigh exactly 16 oz. Inspectors want to develop process control charts. They take five boxes of five bottles each and weigh them. They obtain the following data. The mean weights of each of the 5 samples are 15.2, 14.6, 16.5, 18.1, and 13.2 respectively. Likewise, the range values for the each of 5 samples are 0.4, 0.2, 0.4,0.5, and 0.9 respectively. For the X-bar charts and R-charts, the Parameters, A2, D3 and D4 are respectively. a. 0.37,0.14, 1.86 b. 0.25, 0.31, 1.69 С. 0.73,0.00, 2.28 d. None of them e. 0.58, 0.00, 2.11