A company is producing a high-volume item that sells for $0.75 per unit. The variableproduction 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 () of 1,000 grams and astandard deviation () of 40 grams. Because of the large standard deviation (with respect to thespecification 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 of10,000,000 units produced are nonconforming and cannot be sold without being reworked.

Assume that nonconforming units can be reworked to specification at an additional fixedcost 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 newfilling machine. The new machine will be capable of dispensing the product with weights followinga normal distribution with = 1,000 grams and = 20 grams. As a result, the percent of

nonconforming units will be reduced to 1.24% of production. The new machine will cost $710,000and will last for at least five years. At the end of five years, this machine can be sold for $100,000.

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A. Summary of Case study

B. Cite the problem.