Recall one of the first case studies we explored was for retail manufacturer Zara. Zara primarily serves a non$-$US market $($Europe and Latin America$).$ They have two manufacturing locations: one in Asia $($China$)$ and one in Europe $($Spain$).$ These locations are used to satisfy the retail demand in the European market. Assume that the current demand is $1\mathrm{.}9$ million units. Demand is expected to stay at the same level over the foreseeable future. Each facility has a capacity of $1$ million units per year. With the current exchange rates, the production and distribution cost from Spain is $10$ euros per unit, whereas the production and distribution cost from China is $7$ euros. Over each of the next three years, the Chinese currency could rise relative to the euro by $15$ percent with a probability of $0\mathrm{.}35$ or drop by $5$ percent with a probability of $0\mathrm{.}65.$ An option being considered is to shut down $0\mathrm{.}5$ million units of capacity in Spain and move it to China at a one$-$time cost of $2$ million euros.

a$)$ Do you recommend this option? Assume a discount factor of $10$ percent over the three years in your analysis.

b$)$ Define the range for the probability of the currency increasing, by which your solution in part a is still optimal and show a graph of the expected cost over that range.