Coren Chemical, Inc. develops industrial chemicals that are used by other manufacturers to produce photographic chemicals, preservatives, and lubricants. One of their products, K-1000, is used by several photographic companies to make a chemical that is used in the film-development process. To produce K-1000 efficiently, Coren Chemical uses the batch approach, in which a certain number of gallons are produced at one time. This reduces setup costs and allows Coren Chemical to produce K-1000 at a competitive price. Unfortunately, K-1000 has a very short shelf life of about one month.

Coren Chemical produces K-1000 in batches of 500 gallons, 1000 gallons, 1500 gallons, and 2000 gallons. Using historical data, David Coren was able to determine that the probability of selling 500 gallons of K-1000 is .2. The probabilities of selling 1000, 1500, and 2000 are .3, .4, .1, respectively. The question facing David is how many gallons to produce of K-1000 in the next batch run. K-1000 sells for $20 per gallon. Manufacturing costs is $12 per gallon, and handling costs and warehousing costs are estimated to be $1 per gallon. In the past, David has allocated advertising costs to K-1000 at $3 per gallon. If K-1000 is not sold after the batch run, the chemical loses much of its important properties as a developer. It can, however, be sold at salvage value of $13 per gallon. Furthermore, David has guaranteed to his suppliers that there will always be an adequate supply of K-1000. If David does run out, he has agreed to purchase a comparable chemical from a competitor at $25 per gallon. David sells all the chemical at $20 per gallon, so his shortage means that David loses the $5 to buy the more expensive chemical.

a) Develop a decision tree of this problem