Problem
Over 36 million Americans have migraines, more than the number who have diabetes and asthma combined. Many of them have chronic migraine, meaning they endure disabling symptoms almost every day robbing them of a full life as family members, employees, and productive members of society. Assume demand for the migraine drug Naproxen during the current year is 50,000, and assume demand will grow at 5% a year. If you build a plant that can produce x units of Naproxen per year, it will cost $16x. Each unit of Naproxen is sold for $3. Each unit of Naproxen produced incurs a variable production cost of $0.20 and a variable operation cost of $0.40. Determine how large a Naproxen plant to build to maximize expected profit over the next 10 years.