Show your solution using the decision tree analysis.

1. A construction manager has to decide whether to prepare bid or not. It costs 10,000 to prepare the bid. If the bid is submitted, the probability of contract awarding is 50%. If the Company is awarded the contract, it may earn an income of 200,000 if it succeeds or pay a fine of 18,000 if it fails. The probability of success is 80%. Should the engineer prepare the bid?

2. The production analyst of Unilever is faced with deciding whether to purchase a patent to develop a new product or not. If the company purchases the patent, it should develop the product. The Selling price of the patent is 75,000. There are two ways of developing the product: The electronic system and the manual. It costs 60,000 to use the electronic system, and 40,000 to use the manual. The probability of success in the electronic system is 65% and that in the manual system is 75%. If the product is successfully developed, it will give an income of 800,000. Should the company purchase the patent?

If so, what system of development is best use?

3. The manufacturer, WanTo3 produces products that have a probability to be defective.

These products are divided into batches of 200. Past experience reveals that some (batches) are of good quality (i.e. p=0.05) and some are of bad quality (i.e. p=0.25). In addition, 80% of the batches produced are of good quality and 20% of the batches are of bad quality. These products are then used in an assembly, and before the final assembly leaves the factory, their consistency is finally determined. At a gross average cost of 15 per item, the manufacturer may either screen each item in a batch and replace defective products, or use the items directly without screening. Ultimately, if the latter action is taken, the rework cost is 150 per defective product. For these data, the costs per batch can be calculated as follows:

p = 0.05 p = 0.25

Screen 3000 3000

Do not Screen 1500 7500

Because screening requires inspectors and equipment scheduling, it is important to make the decision to screen or not to screen 2 days before the proposed screening takes place.

However, manufacturers can take one item from a batch and submit it to a laboratory, and it is possible to report the test results (defective or non-defective) before making the screen/no-screen decision. The tested object is returned to its batch following the laboratory examination. The cost of this initial inspection is 175. Also note that the probability that a random sample item is defective is

0.8 * 0.05 + 0.2 * 0.25 = 0.09,

and the probability that an item in a lot is of good quality given a randomly sampled item is defective is 0.444 and the probability that an item in a lot is of good quality given a randomly sampled item is not defective is 0.835. The manufacture wants to minimize his or her cost.