A factory manager must decide whether to stock a particular spare part. The part is absolutely essential to the operation of certain machines in the plant. Stocking the part costs $10 per day in storage and cost of capital. If the part is in stock, a broken machine can be repaired immediately, but if the part is not in stock, it takes one day to get the part from the distributor, during which time the broken machine sits idle. The cost of idling one machine for a day is $65. There are 50 machines in the plant that require this particular part. The probability that any one of them will break and require the part to be replaced on any day is only 0.004 (regardless of how long since the part was previously replaced). The machines break down independently of one another. • (a) If you want to use a probability distribution for the number of machines that break down on a given day, would you use the binomial or Poisson distribution? Why? • (b) Whichever theoretical distribution you chose in part (a), what are appropriate parameters? That is, if you chose the binomial, what are the values for p and n? If you chose the Poisson, what is the value for m? 2 • (c) If the plant manager wants to minimize his expected cost, should he keep zero, one, or two parts in stock? Draw a decision tree and solve the managers problem. (Do not forget that more than one machine can fail in one day!)

Stresses can influence peoples health. Too much  

Vision Rx20 stress can lead to some problems. Such as peoples faces necks shoulders etc may suffer from some problems for the sake of stresses. One very typical example is peoples eyes. It is known that peoples eyes are composed of some muscles and too much stresses can make them tightened. If that happens people may suffer from eye problems. Then how to solve these problems caused by stress The best way is swinging. Swinging can help to relax many muscles such as eye muscles shoulder muscles etc. some specialists hold that if people can swing some time everyday they can have sound health and nice visions. This is suitable for anyone.

Before starting the exercise people should find a window. Then they should make sure that their legs and arms should not put together. Then they can turn their upper bodies in the right until they can not turn any more. After that turn back to the left. This is really very simple. Several minutes later people may find that they are relaxed to some degree. This process can help people to relax their eyes too. When looking at the windows peoples eyes can be relaxed like many other parts of the bodies. One point should be noticed that people are not suggested to look at anything outside. What they need do is to scan. For the eyes are trying to focus on something they may get blurred.

During the process people should keep their spine straight and arms loose for any posture. The most magic point is this method can help people to get their spines back to normal shape. It can also assure that people are no longer in need of other exercises in their spines people with spine problems in particular. If it is needed people are suggested to do this exercise twice a day especially when they get up and go sleep. This can help people to relax themselves to a great extent. A nice day and sound sleep can thus be promised. Still more people should also learn to relax their eyes.

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