Roll-Tech Corporation (RTC) wants to begin producing and selling one of its products in Eastern Europe. Because of the nature of the production process, manufacturing plants can only be built with a capacity of 100,000 units per year, at a cost of $5 million, or 250,000 units per year, at a cost of $10 million. RTC is uncertain about the demand for the product in Eastern Europe, but it estimates that annual demand will be 50,000, 150,000, or 250,000 units, with probabilities of 0.2, 0.6, and 0.2 respectively. If a 100,000 unit plant is built, the expected lifetime profits (not counting the $5 million construction cost) will be $2 million, $8 million, or $8 million, according to whether demand is 50,000, 150,000 or 250,000 per year. With a 250,000 unit plant the lifetime profits (not counting the $10 million construction cost) will be $1 million, $12 million, or $20 million for the three demand outcomes. Which plant capacity will maximize expected lifetime profits, including construction costs?
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