Reference no: EM132518072
A company is producing a high-volume item that sells for $0.75 per unit. The variable production cost is $0.30 per unit. The company is able to produce and sell 10,000,000 items per year when operating at full capacity.
The critical attribute for this product is weight. The target value for weight is 1,000 grams, and the specification limits are set at ±50 grams. The filling machine used to dispense the product is capable of weights following a normal distribution with an average (µ) of 1,000 grams and a standard deviation (σ) of 40 grams. Because of the large standard deviation (with respect to the specification limits), 21.12% of all units produced are not within the specification limits. (They either weigh less than 950 grams or more than 1,050 grams.) This means that 2,112,000 out of 10,000,000 units produced are nonconforming and cannot be sold without being reworked.
Assume that nonconforming units can be reworked to specification at an additional fixed cost of $0.10 per unit. Reworked units can be sold for $0.75 per unit. It has been estimated that the demand for this product will remain at 10,000,000 units per year for the next five years.
To improve the quality of this product, the company is considering the purchase of a new filling machine. The new machine will be capable of dispensing the product with weights following a normal distribution with µ = 1,000 grams and σ = 20 grams. As a result, the percent of
nonconforming units will be reduced to 1.24% of production. The new machine will cost $710,000 and will last for at least five years. At the end of five years, this machine can be sold for $100,000.
A. Summary of Case study
B. Cite the problem.