An automotive manufacturer is setting up capacity in China and North America for the next 2 years. The annual demand in each market is 3 thousand automobiles and it is likely to increase by 10% with a probability 0.8 and stay the same with a probability 0.2. The two choices under consideration are building 8 thousand units (automobiles) of capacity in North America; or building 4 thousand units of capacity in each of these two locations. Building 2 plants will occur an additional one-time cost of $40 million. The variable cost of building in North America is (for either small or large plants) is $10,000/automobile, while the cost is China is 80,000 Yuan/automobile. Shipping an automobile from North America to China (and vice versa) costs $500. The current exchange rate is $1 for 9 Yuan. Over the next 2 years, the dollar is expected to strengthen by 15% with a probability 0.4, weaken by 5% with probability 0.4, and remain the same with a probability 0.2. Discount rate k = 0.1

What should this manufacturer do? At what initial cost differential from building the two plants will the auto manufacturer be indifferent between the two options? Use a decision tree to model/ solve this problem.