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A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being 0.25, 0.40, and 0.35, respectively. A small facility is expected to earn an after-tax net present value of $16,000 if demand is low. If demand is average, the small facility is expected to earn $80,000; it can be expanded to medium size to earn a net present value of $59,000. If demand is high, the small facility is expected to earn $80,000 and can be expanded to medium size to earn $60,000 or to large size to earn $129,000. A medium-sized facility is expected to lose an estimated $21,000 if demand is low and earn $143,000 if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of $148,000; it can be expanded to a large size for a net payoff of $146,000. If a large facility is built and demand is high, earnings are expected to be $217,000. If demand is average for the large facility, the present value is expected to be $126,000; if demand is low, the facility is expected to lose $57,000. Draw a decision tree for the three options as described above and calculate the expected payoffs of each option. What size facility should management build to achieve the highest expected payoff?