A chemical manufacturer is setting up capacity in Europe and North America for the next three years. Annual demand in each market is $2$ million kilograms $($kg$)$ and is likely to stay at that level. The two choices under consideration are building $4$ million units of capacity in North America or building $2$ million units of capacity in each of the two loca$-$tions. Building two plants will incur an additional one$-$time cost of $$2$ million. The variable cost of production in North America $($for either a large or a small plant$)$ is currently $$10/$kg$,$ whereas the cost in Europe is $9$ euro$/$kg$.$ The cur$-$rent exchange rate is $1$ euro for U$.$S$.$ $$1\mathrm{.}33.$ Over each of the next three years, the dollar is expected to strengthen by $10$ percent, with a probability of $0\mathrm{.}5,$ or weaken by $5$ per$-$cent, with a probability of $0\mathrm{.}5.$ Assume a discount factor of $10$ percent.

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