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Decision Tree Analysis

As per the given demand scenarios, the demand can be 25,000 (D1), 60,000 (D2) or 100,000 (D3) with probabilities 0.30 (P1), 0.40 (P2) and 0.30 (P3) respectively. For each of the demand scenarios the Artek Manufacturing can exercise any of the two manufacturing capacity options and therefore the expected value of the manufacturing cost will vary as per the chosen capacity option and the uncertain demand scenario. The above situation can be represented by the following decision tree.

The value for ‘option1,’ with the first demand scenario D1 is: $ 550,000 which has the probability 0.30 to occur and so on. Analyzing the above decision tree, the value of uncertain outcomes (the nodes) can be obtained by multiplying the value of the outcomes by their probability. The total for that node of the tree is the total of these values.
Therefore, the total expected cost associated with Option 1 is given as:
0.30 (550,000) + 0.40 (620,000) + 0.30 (700,000) = 165,000+ 248,000+ 210,000 =$ 623,000
The total expected cost associated with capacity option 2 is given as:
0.30 (350,000) + 0.40 (700,000) + 0.30 (1,100,000) = 105,000+ 280,000+ 330,000 =$ 715,000

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Hence, comparing the expected costs for the two capacity options it is ascertained that the expected cost for the first capacity option is lesser than the second one or the first option would be preferred owing to its less cost.