Clearwater Ltd is in the development stage of a newly developed product that purifies household tap water. The product is codenamed Fountain and was developed by one of its own research laboratories. Clearwater is yet to decide on whether to continue with the possibly costly process of bringing it to market. The next step would be test marketing which would cost k$250 and the current estimate of Fountain passing this test is only about 30%. If Fountain is successful at the test market stage, then the company faces a further decision relating to the size of the production plant. A small plant has capacity to produce 30000 units per year and will cost k$750 to build while a large plant has capacity to produce 48000 units per year and costs k$1100. The marketing department has estimated that there is a 40% chance that the main competing company will respond with a similar but not identical product. Clearwater will not know about the response of the competitor until after the building of the plant. This competition will affect the selling price of fountain as well as the demand. The table below summarizes the likely outcomes. The unit prices are in the shaded cells. Large Plant Small Plant Demand (1000) Competition $30 $35 40 No Competition $55 $65 50 Capacity (1000) 48 Setup Cost k$1100 k$750 30 These figures allow us to calculate the marginal revenue for each of the two plant types and for each of the two possible responses of the competition. For instance, if we choose the small plant and there is competition then the demand will be 40000 but we will only be able to satisfy 30000 at a price of $35 and so the marginal revenue is 30,000 $35=$1,050,000. We can similarly calculate the marginal revenue for the other 3 possible cases. a. Draw the decision tree for this problem and make a recommendation for the best decision. b. What values for the probability of successful test marketing and the competition responding make the mean value associated with all possible decisions exactly equal? Give the answers to three decimal places