1). The board of directors (BOD) is considering whether or not to construct a processing plant in Darwin, Northern Territory. Pork Bellies will have an arrangement with the council to use the port for 5 years at a rate of 50% on normal cost and after that the cost will increase 175%. If demand is favorable, Pork Bellies will realize a net profit of $2,000,000 after the 5 years. If the market is not favorable, then they could lose $800,000. At this stage there is no reliable data on how successful the project could be. The board of directors are working on a 50-50 chance that the processing plant will be successful.

1. Construct a decision tree to analyze the problem. What should the BOD do, justify your answer? 

2. The BOD are not confident with a 50-50 approach and have decided to employ a research firm who specialize in Bayesian Theorem to conduct a study on the viability of constructing a processing plant. The study will cost $10,000 and will work on the following statements of probability:

   Probability of a favorable market given a favorable study = 0.72

   Probability of an unfavorable market given a favorable study = 0.28

   Probability of a favorable market given an unfavorable study = 0.21

   Probability of unfavorable market given an unfavorable study = 0.79

   Probability of a favorable research study = 0.55

   Probability of an unfavorable research study = 0.45

   1. Develop a decision tree to reflect the new alternatives. 
   2. Using the EMV approach, recommend a strategy that BOD should take. In your response discuss the alternatives. 
   3. Using the expected value of sample information, how much would the BOD be prepared to pay for the study? 
   4. What other information would the BOD want to help in making their decision?
3. 
   
4. 2). Pork Bellies is concerned that not enough space has been allocated for ships to dock and load quickly. You have been asked to create a simulation based on the following information:

   Hours between arrivals	Relative frequency
   1	0.06
   2	0.12
   3	0.19
   4	0.21
   5	0.23
   6	0.11
   7	0.08

   Hours to load	Relative frequency
   3	0.4
   4	0.3
   5	0.2
   6	0.1

   The port works 7 days a week and 24 hours a day.

   Required:

   1. Using a table of random numbers simulate 2 weeks where only 1 ship can dock and load at a time. 
   2. Based on your results, should Pork Bellies try to acquire a second dock to unload? Justify your answer by discussing the results of the simulation, taking into consideration other factors that will impact the decision.