The Watts New Lightbulb Corporation ships large consignments of lightbulbs to big in- dustrial users. When the production process is functioning correctly (which is 90% of the time), 10% of all bulbs produced are defective. However, the process is susceptible to an occasional malfunction, leading to a defective rate of 20%. The Watts New Lightbulb Corporation counts the cost, in terms of goodwill, of a shipment with the higher defective rate to an industrial user as $5,000. If a consignment is suspected to contain this larger proportion of defectives, it can instead be sold to a chain of discount stores, though this in- volves a reduction of $600 in profits, whether or not the consignment does indeed contain a large proportion of defective bulbs. Decisions by this company are made through the EMV criterion.

(a) A consignment is produced. In the absence of any further information, should it be shipped to an industrial user or to the discount chain?

(b) Suppose that a single bulb from the consignment is checked. Determine where the consignment should be shipped under each of the following circumstances: (i) This bulb is defective. (ii) This bulb is not defective.

(c) Suppose that two bulbs from the consignment are checked. Determine where the con- signment should be shipped for each of the following situations: (i) Both bulbs are defective. (ii) Just one bulb is defective. (iii) Neither bulb is defective.

(d) Without doing the calculations, indicate how the decision problem could be attacked if 100 bulbs were checked prior to shipping the consignment.